One question, is a circle with infinite diamater a square? I am guessing that the bigger a circle gets, the lesser the edge's curved. If so, then would a circle of infinite length would actually be a square? Or would it just be a line that goes no-where forever?
I'm puzzled because a friend of mine believes that the Universe is infinite.
There are no edges on a circle, by definition. If it gets an edge, it's no longer a circle.
As a circle's diameter approaches infinity, it remains a circle.
As a circle's diameter approaches infinity, it remains a circle.
QUOTE (El_Machinae+Mar 25 2006, 01:02 AM)
There are no edges on a circle, by definition. If it gets an edge, it's no longer a circle.
As a circle's diameter approaches infinity, it remains a circle.
When you say "edge" do you mean "corner"?
Back to the circle - I thought the circumference of an infinitely large circle was a straight line.
Also if its diameter is a real number then the infinitely large circle will be infinitely bigger
than if its diameter were an infinitely large whole number.
Does that mean some some straight lines are straighter than others?
As a circle's diameter approaches infinity, it remains a circle.
When you say "edge" do you mean "corner"?
Back to the circle - I thought the circumference of an infinitely large circle was a straight line.
Also if its diameter is a real number then the infinitely large circle will be infinitely bigger
than if its diameter were an infinitely large whole number.
Does that mean some some straight lines are straighter than others?
Perhaps the limit it is approaching is a straight line? So if it is infinite, then it would be the ultimately straight line? 
QUOTE
When you say "edge" do you mean "corner"?
Yeah.
As a circle gets larger, the line gets straighter. The idea of a circle with an infinite diameter is not viable though. Overtime, though, the line would get straighter.
What does this have to do with the universe being infinite in size?
An infinite universe has no bounds whereas the idea of a circle (or sphere) implies a boundary or outer limit.
curvature is a phenomena of perception. standing in the middle of the desert, or ocean (on a boat), you cant really tell that the horizon has a curve. it looks like a straight line. however, if you were to move above that 2D surface into the third spatial dimension, then you would gradually see that the straight line of the horizon is indeed curved. so i guess depending on your position from the ever expanding circle would determine the degree of curvature.
but yes, standing in the desert as the circle (horizon) gets larger, the limit of the curve would be the straight line
but yes, standing in the desert as the circle (horizon) gets larger, the limit of the curve would be the straight line
Condraz23 you are a genius! Yes an infinite circle is actually a square and the universe is a cube (the idea is so cool you would be stupid not to believe it) I knew that the universe was a cube before I read your question but now I know why its a cube.
Now what was I thinking about again? Meh, probably something amusing
Now what was I thinking about again? Meh, probably something amusing
El_Machinae approaching infinity and being infinite are 2 infinitly different things 
Infinity has no shape or boundries,it is infinite. We human-being's cannot comprehend mentally such an enity or even attempt to isolate---
it's properties or understand it has no equation to deal with. That mystery belongs to God,Our Creator and The Great Revealer.
it's properties or understand it has no equation to deal with. That mystery belongs to God,Our Creator and The Great Revealer.
Su-Moon this is in Revelations last few pages "and Gods perfect city would be laid out as a square. 1500 miles high 1500 miles long 1500 miles deep using human measurements wich are also angelic measurements"
CHECKMATE
CHECKMATE
Ncholas of Cusa was interested in an infinite circle. He recognized that its arc would be a straight light. I think he lived in the 1500's.
You guys! If God had "Dimensions" to his perfect city, he wouldnt BE God. WHen will you people realize God is in the living man; you've never died, your just picking up these biological instruments of destiny... YOU and you alone wanted to be here on this physical plane of reality. This place is OUR creation, and we've all got our hand at it.
If God were God, then the God wouldn't have to worshipped... down on your knees sinner!
If God were God, then the God would not be an insecure, revengeful, warlord.
If God were God, then the God wouldnt require ANYTHING of you, but simply 'TO BE'
If God were the God you've heard so much about... well you wouldnt be here.
I am God You are God You won't torched its ok
SO be it!
zero
If God were God, then the God wouldn't have to worshipped... down on your knees sinner!
If God were God, then the God would not be an insecure, revengeful, warlord.
If God were God, then the God wouldnt require ANYTHING of you, but simply 'TO BE'
If God were the God you've heard so much about... well you wouldnt be here.
I am God You are God You won't torched its ok
SO be it!
zero
I seem to remember Good Elf mentioning something like: as an object approaches c it's apparent trajectory veers towards 90 degrees to its path.....could this be envisaged as an effect of curvature increase.....the greater the velocity the smaller the universe?
QUOTE
If God were God, then the God wouldn't have to worshipped... down on your knees sinner!
If God were God, then the God would not be an insecure, revengeful, warlord.
If God were God, then the God wouldnt require ANYTHING of you, but simply 'TO BE'
If God were the God you've heard so much about... well you wouldnt be here.
If God were God, then the God would not be an insecure, revengeful, warlord.
If God were God, then the God wouldnt require ANYTHING of you, but simply 'TO BE'
If God were the God you've heard so much about... well you wouldnt be here.
*** zeropointbug I couldnt have put it better myself (although The LORD is still my most favourite fictional character) But keep in mind that doesnt nessesarily mean that insecure, vengful, warlord we have heard so much about doesnt exist. So heres some advice...watch your mouth
Warlord?
You must be talking muslim God
Or old testament
You must be talking muslim God
Or old testament
Nick, yeah im talking about the Old Testament God
What about Christ? From what I understand he died so that we wouldn't have to. At least not unnecesarily. By the way I don't think Christ was God. He was the son.
Nick if your interested in the topic of the Old and New testament (Im way past 7:30) Gods read up on gnostic Christianity. Truly Truly I say to you they have the real story. But lets get back to the real topic. There is no such thing as an infinite circle...its actually a square! The universe is a cube people! Humour me. What a total slap in the face wouldnt you agree? Where do you see a straight line anywhere in nature? Wide is the path to destruction but narrow is the path to salvation. I said it before and ill say it again. A cube? Its so cool you would be stupid not to believe it or at least give this idea a second glance.
I got more game than a bitch got curves
I got more game than a bitch got curves
Have you ever heard of Squaring the Circle?
You must be Holy beause I AM Holy (this is not a qoute)
Question-Is a circle with an infinite diameter a square? People the shape of the universe is a cube.....Now what was I thinking about again? Ahh I'm sure it was something amusing
duct tape rope nigga......duct tape rope
Question-Is a circle with an infinite diameter a square? People the shape of the universe is a cube.....Now what was I thinking about again? Ahh I'm sure it was something amusing
duct tape rope nigga......duct tape rope
Hi fivedoughnut et al,
QUOTE (fivedoughnut Posted on May 28 2006+ 03:14 AM)
I seem to remember Good Elf mentioning something like: as an object approaches c it's apparent trajectory veers towards 90 degrees to its path.....could this be envisaged as an effect of curvature increase.....the greater the velocity the smaller the universe?
This was about relativity being a rotation rather than a contraction, the path of linear motion rotates away from all observers by an angle arcsine(V/C). This is how if a surface on a light cone was spinning then... as R the radius increased... the greater the length contraction (rotation away from all other spatial directions and observers into higher dimensions). A relativistic "bubble" would form whose external size is not volumetrically related to the interior volume by pi. Effectively the circumference of a circle at an interior distance R is less than the circumference of a non-spinning circle, since length contraction has occurred along the direction of motion tangentially.
Alternatively, and more importantly, if this was happening in higher dimensions this solid spin could occur on three orthogonal planes simultaneously without disturbing the "contents". this would eventually "nip off" a bubble whose interior space could be any size you nominate and the external surface area could be made as small as you nominate, effectively a "tiny bubble" universe. The only provisos are this spinning stuff is not made of material particles but of the very space itself and this must be in higher dimensions to support three planar two dimensional surfaces... (x, ix) (y, iy) and (z, iz) each made of a real and an imaginary dimension "pair"... a complex volumetric space not seen in our "spacetime" made of an additional six dimensions in total. You could also think of this as two additional "semi-compact" orthogonal three spaces like our own "spacetime"... only very tiny.
What would happen is when sub-atomic particles are created through particle anti-particle reactions from high energy photon pairs these spaces are formed spontaneously and they are the particles and they exist in actually the six higher dimensions of a "string space" but share three other dimensions with us which altogether are our 9 dimensional spin space and one dimension of time (10 dimensions). An 11th dimension is also required as an internal space to provide a means by which all strings can propagate and communicate in those higher dimensions
In such a space the little sub-universe has been "inflated" by spin energy and stabilized with the laws of CPT symmetry. C = Charge conjugation, P = Parity or mirror symmetry, and T = temporal symmetry (in time). This is my "Party Clown" view of the Universe that sees absolutely everything in our universe are the result of these little dimensional balloons from which we are able to construct everything else with the help of "Dirac's Party Trick" and the properties of bosons and fermions.
Of course there is more to it than this but this is the fundamentals. Inside the "hypersurfaces" of such "universes" the geometry is such that as you draw larger and larger circles of ever greater R is like drawing circles on the inside of a sphere (or inner wall of a balloon... a brane) of ever increasing R, after a certain point the "circle" is still topologically circumscribing the "center" but eventually the circle is actually "contracting" around another point that does not contain the original center. If you keep going with increasing the radius of the sphere you will find that this will "contract" away until it disappears into the "infinitely small".
It is my belief that this is the true geometry of our Universe and explains much about the existing laws of physics and the ultimate origin of the quantum.
Cheers
Alternatively, and more importantly, if this was happening in higher dimensions this solid spin could occur on three orthogonal planes simultaneously without disturbing the "contents". this would eventually "nip off" a bubble whose interior space could be any size you nominate and the external surface area could be made as small as you nominate, effectively a "tiny bubble" universe. The only provisos are this spinning stuff is not made of material particles but of the very space itself and this must be in higher dimensions to support three planar two dimensional surfaces... (x, ix) (y, iy) and (z, iz) each made of a real and an imaginary dimension "pair"... a complex volumetric space not seen in our "spacetime" made of an additional six dimensions in total. You could also think of this as two additional "semi-compact" orthogonal three spaces like our own "spacetime"... only very tiny.
What would happen is when sub-atomic particles are created through particle anti-particle reactions from high energy photon pairs these spaces are formed spontaneously and they are the particles and they exist in actually the six higher dimensions of a "string space" but share three other dimensions with us which altogether are our 9 dimensional spin space and one dimension of time (10 dimensions). An 11th dimension is also required as an internal space to provide a means by which all strings can propagate and communicate in those higher dimensions
In such a space the little sub-universe has been "inflated" by spin energy and stabilized with the laws of CPT symmetry. C = Charge conjugation, P = Parity or mirror symmetry, and T = temporal symmetry (in time). This is my "Party Clown" view of the Universe that sees absolutely everything in our universe are the result of these little dimensional balloons from which we are able to construct everything else with the help of "Dirac's Party Trick" and the properties of bosons and fermions.
Of course there is more to it than this but this is the fundamentals. Inside the "hypersurfaces" of such "universes" the geometry is such that as you draw larger and larger circles of ever greater R is like drawing circles on the inside of a sphere (or inner wall of a balloon... a brane) of ever increasing R, after a certain point the "circle" is still topologically circumscribing the "center" but eventually the circle is actually "contracting" around another point that does not contain the original center. If you keep going with increasing the radius of the sphere you will find that this will "contract" away until it disappears into the "infinitely small".
It is my belief that this is the true geometry of our Universe and explains much about the existing laws of physics and the ultimate origin of the quantum.
Cheers
There is no such thing as an infinite circle. A circle by definition is a specific 2-dimensional shape comprised of circumference, radius, and diameter. If a circle is "infinite", it is no longer a circle. All circles have size.
This whole question about whether the circumference gets straighter is pointless, because the answer is relative. If the circle in comparison to you is much larger, then the circumference will appear to get straighter. However, if the circle in comparison to you is smaller, then the circumference will appear to have an extreme curvature. Remember, every physically measurable thing in this universe is relative to another. The only reason a circle is larger than another is because another circle exists. If there weren't two circles (or any people, for that matter) by which to measure another one, then you simply couldn't measure that circle.
It's all about relativity.
This whole question about whether the circumference gets straighter is pointless, because the answer is relative. If the circle in comparison to you is much larger, then the circumference will appear to get straighter. However, if the circle in comparison to you is smaller, then the circumference will appear to have an extreme curvature. Remember, every physically measurable thing in this universe is relative to another. The only reason a circle is larger than another is because another circle exists. If there weren't two circles (or any people, for that matter) by which to measure another one, then you simply couldn't measure that circle.
It's all about relativity.
Hi TheGuyWithAnswers,
What you say has some truth but, since the question is "interesting", we are widening this discussion for the sake of "curiosity" from there. Maybe there are no "infinite" circles but it is interesting to consider such geometries. Consider the universe (a two dimensional version of it) being on the inside surface of a closed sphere (like the inside of a party balloon). Lets draw a "circle" on the inside around a single point there. I am reminded that the definition of a circle is a figure described as the locus of all points "equidistant" from a single point. Then draw larger and larger concentric circles in that geometry, whose radii (distance from the center) increases incrementally. What eventually happens? We find that the circumference is no longer 2*pi*r and the "circle" converges around another more distant point. Now what is the circle here and where is its center? There are some aspects of our "real" Universe that have just this kind of "anti-social" behavior. A rather weird party balloon might even have this locus converge to a "square"... heaven forbid... he he he!
Cheers
What you say has some truth but, since the question is "interesting", we are widening this discussion for the sake of "curiosity" from there. Maybe there are no "infinite" circles but it is interesting to consider such geometries. Consider the universe (a two dimensional version of it) being on the inside surface of a closed sphere (like the inside of a party balloon). Lets draw a "circle" on the inside around a single point there. I am reminded that the definition of a circle is a figure described as the locus of all points "equidistant" from a single point. Then draw larger and larger concentric circles in that geometry, whose radii (distance from the center) increases incrementally. What eventually happens? We find that the circumference is no longer 2*pi*r and the "circle" converges around another more distant point. Now what is the circle here and where is its center? There are some aspects of our "real" Universe that have just this kind of "anti-social" behavior. A rather weird party balloon might even have this locus converge to a "square"... heaven forbid... he he he!
Cheers
QUOTE (Good Elf+Jun 4 2006, 05:44 AM)
Of course there is more to it than this but this is the fundamentals. Inside the "hypersurfaces" of such "universes" the geometry is such that as you draw larger and larger circles of ever greater R is like drawing circles on the inside of a sphere (or inner wall of a balloon... a brane) of ever increasing R, after a certain point the "circle" is still topologically circumscribing the "center" but eventually the circle is actually "contracting" around another point that does not contain the original center. If you keep going with increasing the radius of the sphere you will find that this will "contract" away until it disappears into the "infinitely small".
It is my belief that this is the true geometry of our Universe and explains much about the existing laws of physics and the ultimate origin of the quantum.
Cheers
The universe is a hypersurface of a 4Sphere. This hypersphere is growing. Space is stretching inbetween the galaxies. We are moving away from the center of the 4th dimension as the universe expands. The hypersphere was once a singularity. This is called Time Zero.
Matter was created by a one sided quantum fluctuation.
It is my belief that this is the true geometry of our Universe and explains much about the existing laws of physics and the ultimate origin of the quantum.
Cheers
The universe is a hypersurface of a 4Sphere. This hypersphere is growing. Space is stretching inbetween the galaxies. We are moving away from the center of the 4th dimension as the universe expands. The hypersphere was once a singularity. This is called Time Zero.
Matter was created by a one sided quantum fluctuation.
Hi Nick,
QUOTE (Nick Posted on Yesterday at 1:17 PM+)
We are moving away from the center of the 4th dimension
Do not agree. Firstly the "real" 4th dimension is time. In that sense I suppose we are all moving away from zero time. What we see is every point is moving away from every other point (on average), this is Hubble Shift. If we actually had a "big bang" at the center of our universe then this would expand on the surface of a single shell as an explosive shell exploding in space... this is not what we see. Individual stars explode and do this why doesn't the Universe?? 
As to an early singularity being the source of the big bang... if you want to believe that you can but you can't prove it since a singulatrity cannot be analysed to give any data before its creation. "Quantum fluctuations" is a "Magician's Trick" that "explains everything" while explaining nothing.
Cheers
As to an early singularity being the source of the big bang... if you want to believe that you can but you can't prove it since a singulatrity cannot be analysed to give any data before its creation. "Quantum fluctuations" is a "Magician's Trick" that "explains everything" while explaining nothing.Cheers
A straight line is a circle with infinite radius. Thus a straight line is just a subcase of a circle.
Hi Anders Engman,
QUOTE (Anders Engman Posted on Today at 5:08 PM+)
A straight line is a circle with infinite radius. Thus a straight line is just a subcase of a circle.
Not really... topologically speaking what is the meaning of the inside of a straight line?
Cheers
Cheers
What is the equation for infinity? Don't you need that equation to correctly describe an infinite circle? Even if it was a google x google light years wide, we're still in the realm of real numbers. And any real measureable circle will never go to a straight line no matter how big, only approach it. And in that light (sic), it would approach it infinitely (from our point of view) yet still remain a measurable circle. I think that's a more reasonable way to view infinity, not by 'size'. A universe may increase in size infinitely, but it is always finite in size. Infinity makes more sense as a vector than as a quantity.
There can be no point at which a number or a size turns into infinity. If we can't mathematically describe an infinite circle, we certainly can't describe it's characteristics.
If the circle were 'infinitely big', and we were 'infinitely big', would we see infinity curve and be ruled by pi? I think the question is as meaningless as an infinite circle.
There can be no point at which a number or a size turns into infinity. If we can't mathematically describe an infinite circle, we certainly can't describe it's characteristics.
If the circle were 'infinitely big', and we were 'infinitely big', would we see infinity curve and be ruled by pi? I think the question is as meaningless as an infinite circle.
QUOTE (Good Elf+Jun 12 2006, 12:27 AM)
Hi Nick,
QUOTE (Nick Posted on Yesterday at 1:17 PM+)
We are moving away from the center of the 4th dimension
Um, that was the idea. Let me bold the important part...
Um, that was the idea. Let me bold the important part...
If infinity * any number = infinity then
Infinity = pi * infinity
But if infinity = infinity then
Now let me quote the important conclusion....
which is akin to saying 0/0 = 1
Not even close. 0 is 0, infinity is infinity. 0 != infinity which is stated that x/x = 1 when x!=0. So if x=infinity then x!=0 and so x/x = 1.
It's all bad anyway since it is treating infinity like a number. Infinity is not a number and so you can't use it in equations like above. It was hypothetical but you were never interested in that. You simply attack for the sake of attacking. Grabbing at straws along the way.
The whole point of it was to be hypothetical. Not only is infinity/infinity undefined, it is outright bad math because infinity is not a number but is being treated as such. The hint was the if/then's.
Although, considering infinity is not a number, wouldn't that make a circle with an infinite anything impossible.
If the circumference is infinite then that would make the diameter infinite but if the diameter is infinite in length, the edge of the circle (where the circumference would be) would not exist and so the circle would not exist.
After all the circumference of a circle exists at the ends of the diameter but an infinite length diameter is one that has no ends at all. So the circle can not exist.
Briefly running this by my wife she came back with a very simple answer. If an infinite circumference makes the circumference a straight line then you don't have a circle. The circumference of the circle must be curved to form the circle.
Two people walking down a road that has no end. One is ahead of the other. Both walk an infinite distance yet one person has walked farther than the other.
Two people walking down a road that has no end. One is ahead of the other. Both walk an infinite distance yet one person has walked farther than the other.
If they are still walking then they haven't walked an infinite distance, have they?
So you've got a bad example there, PC.
Still treating infinity as some largest quantity I see. If infinity was a reachable destination (which it is not) then once reached they would stop walking but if they stop then they have only traveled a finite distance.
See the paradox that results in treating infinity as something that is reachable. What makes the example represent walking infinity is in the fact that there doesn't exist a finite distance between them and the starting point. As soon as a finite distance is obtained, they have moved on and a larger distance exists. Thus if the distance between them is not finite (because they are still moving) then the distance between them and the starting point is infinite.
Now this is only true because there is no end to the road. They will never stop walking. If there was an end that that would mean at some finite time they will get to a finite distance in which they stop.
However in case that is all too much for you I'll demonstrate another way.
Two people walking down a road that has no end (infinity long) where 1 person is ahead of the other. An infinite amount of time has passed. The two have now walked an infinite distance yet one is still ahead of the other and both are still walking because the road has no end to reach.
However you can't seem to grasp physical demonstration so let's keep it mathematical.
The set of naturals is an infinite set. Aleph_0.
The set of reals is also an infinite set but is not countable. Aleph_1
Aleph_0 < Aleph_1
So you have one infinite set larger than the other. That gives you infinity < infinity.
Also to further demonstrate that a circle with an infinite anything is impossible think of a piece of paper that has an infinite height and length. So there is no edge to the page. You can draw a circle of any finite size but you still can't draw one of infinite size. Where would you start to draw the circumference? You start drawing at the end of what is to be the diameter but a circle with an infinite circumference will have an infinite diameter and so there is no end to begin drawing the circumference.
This goes with any geometric shape. Once you give a dimension an infinite length, you no longer have a geometric shape.
Well you know, it seems to be the only thing you(s) misunderstand so I went with that.
Well you know, it seems to be the only thing you(s) misunderstand so I went with that.
And you are the one talking about it being reachable.
Oh is that so. Please quote me where I say that the two people reach the end of the road that is infinite in length. The only time I mention reaching an end to a road, I specified the road as being finite in length.
I also see you don't even make an attempt at explaining how it is I didn't get the mathematical one.
Will you deny that the cardinality of the set of naturals is Aleph_0 (countably infinite)?
Will you deny that the cardinality of the set of reals is Aleph_1 (not countably infinity)?
Or will you deny Aleph_0 < Aleph_1?
Well you know, it seems to be the only thing you(s) misunderstand so I went with that.
Oh is that so. Please quote me where I say that the two people reach the end of the road that is infinite in length. The only time I mention reaching an end to a road, I specified the road as being finite in length.
You said that they walked an infinite amount of time.
How did they reach that time unless infinity is reachable?
And why do you talk about post secondary stuff like Aleph when you can't grasp primary level stuff like infinity is not a quantity.
And you didn't give a mathematical explanation of anything relevent.
Then number of zeros in 1.000... 10.000... 0.999... and in 9.999... are all Aleph0.
So Aleph0<Aleph1 has nothing to do with anything.
And note it is countably infinite, not countable.
The paper and drawing a circle is back to physical.
Wow, you people are really lost with the idea of Infinity!
'Infinite circle' is an oxymoron. Neither is there any such thing as 'Infinite distance', or even 'direction'. The moment you posit a 'second thing', you are not describing the necessarily Infinite. There can be no 'beginning', nor 'end', to anything considered to be 'Infinite'. The correct dictionary definition is used for the notion of 'without boundaries'.
So, only One truly Infinite thing can exist, and it must thus necessarily exist everwhere. 'Speed' does not apply, as you must posit the idea of at least two discrete 'points' in order for 'speed' to happen. Humans do this erroneously, when we describe the world around us without recognising that everything is interconnected.
Infinity = 1 ...because anything posited to be Infinite can only be One thing, in Reality. '1' is the only number that corresponds to 'non-divideable' (without boundaries), and '0' simply does not exist.
Every'thing' has an inherent element of 'infiniteness' about it...cause/effect - same thing; constantly changing.
What we currently interpret as the 'finite' physical universe, is the momentary appearance of Infinite Space, condensed into 'physicality' - all of these 'appearances' must return to the Infinite (true/pure) wave-state. This is why the 'black holes' at the centres of 'Galaxies' exist.
g.
Yeah and I also said...
Yeah and I also said...
Well you know, it seems to be the only thing you(s) misunderstand so I went with that.
Do you know what aleph_0 and aleph_1 even means.
If the elements of an infinite set are countable (able to be put into a 1:1 with the whole numbers) then it is aleph_0. The first case in which the elements are not countable are aleph_1.
The natural number set is [1, 2, 3, .....] which can be counted...
1->0
2->1
3->2
etc.
The real number set is, well, good luck showing elements where one comes after the other. the best you can do is...
[......,4,....,3,.....,2,.....,1,.....,0,.....,-1,.....,-2,.....,-3,.....,-4,.....]
Between each integer exist an infinite number of decimal numbers. It is impossible to put the set into a 1:1. That is what makes it aleph_1.
Cardinality refers to the size of a set and so the set of reals is a larger set than the set of naturals. Both are infinite and so the result is different size infinities.
Oh and as for the numbers you gave. If the zeros in both 1.0000..... and 10.000.... are elements of a set then you have two infinite sets which are aleph_0.
0.999... only has one 0 so you don't have an infinite set.
9.999... has no 0's at all.
The whole point of treating the terms as elements of a set and demonstrating that you don't get identical sets proves that you can't simply multiply by ten.
The whole point of treating the terms as elements of a set and demonstrating that you don't get identical sets proves that you can't simply multiply by ten.
And both .999...'s are the same,
The fact that you don't get identical sets using summation terms as the elements of said sets proves that the sum you get from each is not an identical sum. They are then not equal. Not the same.
There exists another simple proof. It proves 1 = 2.
There exists another simple proof. It proves 1 = 2.
And someone agreed it had the same aleph_0 and cardinality to it.
Your point? It's called different ordinals.
Say it with me now...
o-r-d-i-n-a-l-s.
Identical sets with have...
1. The same elements
2. The same cardinality
3. The same ordinal
Oh and since you brought this whole thing up. How does it relate to an infinite circle? Let's try keeping the .9r talk in the .9r thread.
Exactly.
Do not agree. Firstly the "real" 4th dimension is time. In that sense I suppose we are all moving away from zero time. What we see is every point is moving away from every other point (on average), this is Hubble Shift. If we actually had a "big bang" at the center of our universe then this would expand on the surface of a single shell as an explosive shell exploding in space... this is not what we see. Individual stars explode and do this why doesn't the Universe?? As to an early singularity being the source of the big bang... if you want to believe that you can but you can't prove it since a singulatrity cannot be analysed to give any data before its creation. "Quantum fluctuations" is a "Magician's Trick" that "explains everything" while explaining nothing.
Cheers
If the universe is closed then it is an hypersphere. The universe is the surface of an expanding hypersphere. The hypersphere was the orginal singularity. Since the universe is expanding the hypersphere is also. We are moving away from the center of the fourth dimension when the universe expands.
The one sided quantum fluctuation that gave birth to matter is yet to be explained.
As to an early singularity being the source of the big bang... if you want to believe that you can but you can't prove it since a singulatrity cannot be analysed to give any data before its creation. "Quantum fluctuations" is a "Magician's Trick" that "explains everything" while explaining nothing.Cheers
If the universe is closed then it is an hypersphere. The universe is the surface of an expanding hypersphere. The hypersphere was the orginal singularity. Since the universe is expanding the hypersphere is also. We are moving away from the center of the fourth dimension when the universe expands.
The one sided quantum fluctuation that gave birth to matter is yet to be explained.
Hi Nick,
The universe is expanding but that is only applied to what we see in it not necessarily to the "edge of the Universe" itself. It is possible that you are right. The questions I posed still remains valid questions... if the Universe has a physical center then if should expand as stated. Here is some recent data of what our Universe looks like...
Physicsweb: A Cosmic Hall of Mirrors (WMAP)
The Universe, while still appearing to be locally a "dimensional flatspace", is apparently a multiply connected toroidal Poincaré dodecahedrally connected spherical space... whew! More simply we seem to be living inside a "cosmic version" of an "Asteroids" video game.
Cheers
The universe is expanding but that is only applied to what we see in it not necessarily to the "edge of the Universe" itself. It is possible that you are right. The questions I posed still remains valid questions... if the Universe has a physical center then if should expand as stated. Here is some recent data of what our Universe looks like...
Physicsweb: A Cosmic Hall of Mirrors (WMAP)
The Universe, while still appearing to be locally a "dimensional flatspace", is apparently a multiply connected toroidal Poincaré dodecahedrally connected spherical space... whew! More simply we seem to be living inside a "cosmic version" of an "Asteroids" video game.
Cheers
QUOTE (Good Elf+Jun 18 2006, 12:34 AM)
Hi Nick,
The universe is expanding but that is only applied to what we see in it not necessarily to the "edge of the Universe" itself. It is possible that you are right. The questions I posed still remains valid questions... if the Universe has a physical center then if should expand as stated. Here is some recent data of what our Universe looks like...
Physicsweb: A Cosmic Hall of Mirrors (WMAP)
The Universe, while still appearing to be locally a "dimensional flatspace", is apparently a multiply connected toroidal Poincaré dodecahedrally connected spherical space... whew! More simply we seem to be living inside a "cosmic version" of an "Asteroids" video game.
Cheers
There is no edge. The only center is in the 4th dimension.
The universe is expanding but that is only applied to what we see in it not necessarily to the "edge of the Universe" itself. It is possible that you are right. The questions I posed still remains valid questions... if the Universe has a physical center then if should expand as stated. Here is some recent data of what our Universe looks like...
Physicsweb: A Cosmic Hall of Mirrors (WMAP)
The Universe, while still appearing to be locally a "dimensional flatspace", is apparently a multiply connected toroidal Poincaré dodecahedrally connected spherical space... whew! More simply we seem to be living inside a "cosmic version" of an "Asteroids" video game.
Cheers
There is no edge. The only center is in the 4th dimension.
A cirlce of infinite diameter would have a radius of half infinite diameter which is still infinite. So if the radius is infinite the diameter would be twice that and so on. Ever expanding circle. That could be the universe. but it would be a sphere of course.
Hi The_Questioner,
Quantum superposition
Of course quantum physics does this all the time but even Feynman thought this was wacky even though he was partially responsible for it. The Universe really does not make these calculations... we do though... and it only indicates we have an error somewhere.
Cheers
QUOTE
A cirlce of infinite diameter would have a radius of half infinite diameter which is still infinite. So if the radius is infinite the diameter would be twice that and so on. Ever expanding circle. That could be the universe. but it would be a sphere of course.
This whole discussion must really come down to what really "is" not what is mathematically "possible". Our Universe is finite unbounded. This means there are no "infinities" around here. That is unless we do something "unphysical" like dividing the length of a physical line into the dimensions of a point... he he he! This is back to the question of "How many angels can dance on the head of a pin"...Quantum superposition
Of course quantum physics does this all the time but even Feynman thought this was wacky even though he was partially responsible for it. The Universe really does not make these calculations... we do though... and it only indicates we have an error somewhere.
Cheers
Well first as someone who lives next to the ocean I can honestly tell you when you are looking out at the horizon where the ocean meets the sky you can notice a slight curve.
What makes a square a square is the two sets of parallel lines who intersect each other at exactly right angles and whose length are all equal.
A circle simply doesn't have this. All a circle has is one side or you could say infinite sides. Since the size of a circle is dependent on it's diameter than if a circle has an infinite diameter than it is still a circle just of infinite size.
What makes a square a square is the two sets of parallel lines who intersect each other at exactly right angles and whose length are all equal.
A circle simply doesn't have this. All a circle has is one side or you could say infinite sides. Since the size of a circle is dependent on it's diameter than if a circle has an infinite diameter than it is still a circle just of infinite size.
What about similarities between linear concepts of time and the "straight" edges of near-infinite circles? If a circle nears infinity but "remains" a circle, that means that a truly straight line is a mathematical impossibility. What we perceive as straight lines in our daily existence are but an illusion, which they become when you realize that they are the edge of a circle which is near-infinite in size.
Couldn't you apply the same logic to a linear concept of time? If time appears linear in our daily lives, it is because it can be explained in truth as a moment in which a perceived energy transfer from point A to point B is occurring between light and matter, anywhere at any point in time throughout the universe. Doesn't this mean that, just like the straight line that appears straight even though it is the edge of an infinite circle, which, hypothetically viewed at correct magnitude, could again appear seemingly curved, TIME can be viewed in a very similar manner. Except with time, since it is inherently linear to begin with (unlike the circle's edge), would utterly fall apart to reveal this:
Despite the illusion that things are simply happening all around us in the universe, and have been and will be forever happening throughout time, if and when all such events could be viewed at a corresponding magnitude (i.e. super sized for infinity) IT WOULD APPEAR THAT EVERYTHING HAPPENED ONCE, ALL AT ONCE, ALL AT THE SAME TIME. And that the line in that one satorical moment, which divides the all of the energy in all of the light in the universe, which we know moves across a "line" and into matter, imbuing it with kinetic force, THAT LINE COULD ALSO ITSELF BE SO INFINITELY RAZOR THIN.
Couldn't you apply the same logic to a linear concept of time? If time appears linear in our daily lives, it is because it can be explained in truth as a moment in which a perceived energy transfer from point A to point B is occurring between light and matter, anywhere at any point in time throughout the universe. Doesn't this mean that, just like the straight line that appears straight even though it is the edge of an infinite circle, which, hypothetically viewed at correct magnitude, could again appear seemingly curved, TIME can be viewed in a very similar manner. Except with time, since it is inherently linear to begin with (unlike the circle's edge), would utterly fall apart to reveal this:
Despite the illusion that things are simply happening all around us in the universe, and have been and will be forever happening throughout time, if and when all such events could be viewed at a corresponding magnitude (i.e. super sized for infinity) IT WOULD APPEAR THAT EVERYTHING HAPPENED ONCE, ALL AT ONCE, ALL AT THE SAME TIME. And that the line in that one satorical moment, which divides the all of the energy in all of the light in the universe, which we know moves across a "line" and into matter, imbuing it with kinetic force, THAT LINE COULD ALSO ITSELF BE SO INFINITELY RAZOR THIN.
What about similarities between linear concepts of time and the "straight" edges of near-infinite circles? If a circle nears infinity but "remains" a circle, that means that a truly straight line is a mathematical impossibility. What we perceive as straight lines in our daily existence are but an illusion, which they become when you realize that they are the edge of a circle which is near-infinite in size.
Couldn't you apply the same logic to a linear concept of time? If time appears linear in our daily lives, it is because it can be explained in truth as a moment in which a perceived energy transfer from point A to point B is occurring between light and matter, anywhere at any point in time throughout the universe. Doesn't this mean that, just like the straight line that appears straight even though it is the edge of an infinite circle, which, hypothetically viewed at correct magnitude, could again appear seemingly curved, TIME can be viewed in a very similar manner. Except with time, since it is inherently linear to begin with (unlike the circle's edge), would utterly fall apart to reveal this:
Despite the illusion that things are simply happening all around us in the universe, and have been and will be forever happening throughout time, if and when all such events could be viewed at a corresponding magnitude (i.e. super sized for infinity) IT WOULD APPEAR THAT EVERYTHING HAPPENED ONCE, ALL AT ONCE, ALL AT THE SAME TIME. And that the line in that one satorical moment, which divides the all of the energy in all of the light in the universe, which we know moves across a "line" and into matter, imbuing it with kinetic force, THAT LINE COULD ALSO ITSELF BE SO INFINITELY RAZOR THIN.
Couldn't you apply the same logic to a linear concept of time? If time appears linear in our daily lives, it is because it can be explained in truth as a moment in which a perceived energy transfer from point A to point B is occurring between light and matter, anywhere at any point in time throughout the universe. Doesn't this mean that, just like the straight line that appears straight even though it is the edge of an infinite circle, which, hypothetically viewed at correct magnitude, could again appear seemingly curved, TIME can be viewed in a very similar manner. Except with time, since it is inherently linear to begin with (unlike the circle's edge), would utterly fall apart to reveal this:
Despite the illusion that things are simply happening all around us in the universe, and have been and will be forever happening throughout time, if and when all such events could be viewed at a corresponding magnitude (i.e. super sized for infinity) IT WOULD APPEAR THAT EVERYTHING HAPPENED ONCE, ALL AT ONCE, ALL AT THE SAME TIME. And that the line in that one satorical moment, which divides the all of the energy in all of the light in the universe, which we know moves across a "line" and into matter, imbuing it with kinetic force, THAT LINE COULD ALSO ITSELF BE SO INFINITELY RAZOR THIN.
QUOTE (primo+May 27 2006, 03:20 AM)
Condraz23 you are a genius! Yes an infinite circle is actually a square and the universe is a cube (the idea is so cool you would be stupid not to believe it) I knew that the universe was a cube before I read your question but now I know why its a cube.
Now what was I thinking about again? Meh, probably something amusing
Primo, are you the webmaster of this site by any chance?
http://timecube.com/
Admittedly though, there's something special about cubes and the fact they're the only shape that can be tessellated perfectly (assuming a repeating universe), but all the current thinking suggests that the universe is a curved manifold.
Now what was I thinking about again? Meh, probably something amusing
Primo, are you the webmaster of this site by any chance?
http://timecube.com/
Admittedly though, there's something special about cubes and the fact they're the only shape that can be tessellated perfectly (assuming a repeating universe), but all the current thinking suggests that the universe is a curved manifold.
Sorry to post on a thread so old, but if any moderators are reading this... Can anyone rename the account of Comdraz23 to something else? (I tried asking for full deletion but I now realize that would be too difficult and would mess up the boards.)
Thanks so much for your co-operation. This website truly is a great website!
Cheers.
-CoolDude
Thanks so much for your co-operation. This website truly is a great website!
Cheers.
-CoolDude
its not a cube, if it was a cube than it wouldn't be a circle, its just a strait line that goes forever and ever never ending and it never reaches the point wear it begins.
Quit calling it a square
Quit calling it a square
Another way to look at it...
C = pi * d
If the diameter is infinite then...
C = pi * infinity
If infinity * any number = infinity then
Infinity = pi * infinity
But if infinity = infinity then
infinity/infinity = pi
pi = 1
So this demonstrates one of two things.
1) There are different infinity such that you can have infinity > infinity.
2) A circle with an infinite diameter is an impossibility and can not exist.
I believe both are true.
C = pi * d
If the diameter is infinite then...
C = pi * infinity
If infinity * any number = infinity then
Infinity = pi * infinity
But if infinity = infinity then
infinity/infinity = pi
pi = 1
So this demonstrates one of two things.
1) There are different infinity such that you can have infinity > infinity.
2) A circle with an infinite diameter is an impossibility and can not exist.
I believe both are true.
QUOTE (Precursor562+May 19 2008, 05:08 PM)
Another way to look at it...
C = pi * d
If the diameter is infinite then...
C = pi * infinity
If infinity * any number = infinity then
Infinity = pi * infinity
But if infinity = infinity then
infinity/infinity = pi
pi = 1
This is about the worst mathematics I've seen for a long time. You assume infinity/infinity = 1 which is akin to saying 0/0 = 1. However, on the other thread you say 0/0=0!
infinity/infinity is undefined. All you need to do to see that is type it into mathematica. If you don't have mathematica I'll do it for you and post a screenshot just so you'll shut up.
C = pi * d
If the diameter is infinite then...
C = pi * infinity
If infinity * any number = infinity then
Infinity = pi * infinity
But if infinity = infinity then
infinity/infinity = pi
pi = 1
This is about the worst mathematics I've seen for a long time. You assume infinity/infinity = 1 which is akin to saying 0/0 = 1. However, on the other thread you say 0/0=0!
infinity/infinity is undefined. All you need to do to see that is type it into mathematica. If you don't have mathematica I'll do it for you and post a screenshot just so you'll shut up.
QUOTE
You assume infinity/infinity = 1
Um, that was the idea. Let me bold the important part...
QUOTE (->
| QUOTE |
| You assume infinity/infinity = 1 |
Um, that was the idea. Let me bold the important part...
If infinity * any number = infinity then
Infinity = pi * infinity
But if infinity = infinity then
Now let me quote the important conclusion....
QUOTE
So this demonstrates one of two things.
1) There are different infinity such that you can have infinity > infinity.
2) A circle with an infinite diameter is an impossibility and can not exist.
I believe both are true.
1) There are different infinity such that you can have infinity > infinity.
2) A circle with an infinite diameter is an impossibility and can not exist.
I believe both are true.
QUOTE (->
| QUOTE |
| So this demonstrates one of two things. 1) There are different infinity such that you can have infinity > infinity. 2) A circle with an infinite diameter is an impossibility and can not exist. I believe both are true. |
which is akin to saying 0/0 = 1
Not even close. 0 is 0, infinity is infinity. 0 != infinity which is stated that x/x = 1 when x!=0. So if x=infinity then x!=0 and so x/x = 1.
It's all bad anyway since it is treating infinity like a number. Infinity is not a number and so you can't use it in equations like above. It was hypothetical but you were never interested in that. You simply attack for the sake of attacking. Grabbing at straws along the way.
QUOTE (Precursor562+May 19 2008, 07:44 PM)
It's all bad anyway since it is treating infinity like a number. Infinity is not a number and so you can't use it in equations like above. It was hypothetical but you were never interested in that. You simply attack for the sake of attacking. Grabbing at straws along the way.
Your conclusions in this context are completely wrong. Sorry.
I'm rather confused by the way that you know something is wrong but you do it anyway. The fact that infinity/infinity is not defined is a direct result of the fact that infinity is not a number. You seem to know that, and yet the broader point escapes you.
If you really had an understanding of this subject, you'd appreciate that infinity/infinity is very similar to 0/0 because the limit of 1/x as x -> 0 is plus or minus infinity. Both quotients are undefined.
As it is, you missed it completely. Poor old you.
Your conclusions in this context are completely wrong. Sorry.
I'm rather confused by the way that you know something is wrong but you do it anyway. The fact that infinity/infinity is not defined is a direct result of the fact that infinity is not a number. You seem to know that, and yet the broader point escapes you.
QUOTE
Not even close. 0 is 0, infinity is infinity. 0 != infinity which is stated that x/x = 1 when x!=0. So if x=infinity then x!=0 and so x/x = 1.
If you really had an understanding of this subject, you'd appreciate that infinity/infinity is very similar to 0/0 because the limit of 1/x as x -> 0 is plus or minus infinity. Both quotients are undefined.
As it is, you missed it completely. Poor old you.
QUOTE (Precursor562+May 19 2008, 05:08 PM)
Another way to look at it...
C = pi * d
If the diameter is infinite then...
C = pi * infinity
If infinity * any number = infinity then
Infinity = pi * infinity
But if infinity = infinity then
infinity/infinity = pi
pi = 1
So this demonstrates one of two things.
1) There are different infinity such that you can have infinity > infinity.
2) A circle with an infinite diameter is an impossibility and can not exist.
I believe both are true.
I'd be embarrassed if my dog typed this. Sure, it might be impressive that a dog learnt how to type, but if it only served as a means to demonstrate that these are the kind of ridiculous thoughts that go through his head, I would prefer that he spend his time licking his bollocks and humping the legs of our dinner table. The latter would give him a far better chance of sustaining intellectual credibility...
C = pi * d
If the diameter is infinite then...
C = pi * infinity
If infinity * any number = infinity then
Infinity = pi * infinity
But if infinity = infinity then
infinity/infinity = pi
pi = 1
So this demonstrates one of two things.
1) There are different infinity such that you can have infinity > infinity.
2) A circle with an infinite diameter is an impossibility and can not exist.
I believe both are true.
I'd be embarrassed if my dog typed this. Sure, it might be impressive that a dog learnt how to type, but if it only served as a means to demonstrate that these are the kind of ridiculous thoughts that go through his head, I would prefer that he spend his time licking his bollocks and humping the legs of our dinner table. The latter would give him a far better chance of sustaining intellectual credibility...
QUOTE
'm rather confused by the way that you know something is wrong but you do it anyway.
The whole point of it was to be hypothetical. Not only is infinity/infinity undefined, it is outright bad math because infinity is not a number but is being treated as such. The hint was the if/then's.
Although, considering infinity is not a number, wouldn't that make a circle with an infinite anything impossible.
If the circumference is infinite then that would make the diameter infinite but if the diameter is infinite in length, the edge of the circle (where the circumference would be) would not exist and so the circle would not exist.
After all the circumference of a circle exists at the ends of the diameter but an infinite length diameter is one that has no ends at all. So the circle can not exist.
Briefly running this by my wife she came back with a very simple answer. If an infinite circumference makes the circumference a straight line then you don't have a circle. The circumference of the circle must be curved to form the circle.
QUOTE (Precursor562+May 19 2008, 12:08 PM)
1) There are different infinity such that you can have infinity > infinity.
2) A circle with an infinite diameter is an impossibility and can not exist.
I believe both are true.
You just said you know you can't treat infinity as a number, yet you believe that you can have infinity > infinity?
2) A circle with an infinite diameter is an impossibility and can not exist.
I believe both are true.
You just said you know you can't treat infinity as a number, yet you believe that you can have infinity > infinity?
Oops.
Yes, there are different infinite sets, some of which have more members than another.
Yes, there are different infinite sets, some of which have more members than another.
QUOTE
You just said you know you can't treat infinity as a number, yet you believe that you can have infinity > infinity?
Two people walking down a road that has no end. One is ahead of the other. Both walk an infinite distance yet one person has walked farther than the other.
QUOTE (Precursor562+May 23 2008, 01:06 AM)
Two people walking down a road that has no end. One is ahead of the other. Both walk an infinite distance yet one person has walked farther than the other.
If they are still walking then they haven't walked an infinite distance, have they?
So you've got a bad example there, PC.
QUOTE (Sapo+May 22 2008, 07:51 PM)
Oops.
Yes, there are different infinite sets, some of which have more members than another.
Well, if you say one infinity has more members than another infinity, wouldn't that make it finite?
I always did hate infinity and infinite series...
Yes, there are different infinite sets, some of which have more members than another.
Well, if you say one infinity has more members than another infinity, wouldn't that make it finite?
I always did hate infinity and infinite series...
QUOTE (NoCleverName+May 23 2008, 05:07 AM)
If they are still walking then they haven't walked an infinite distance, have they?
So you've got a bad example there, PC.
But if they are still walking, the one ahead of the other will always be walking a greater distance than the other.
So you've got a bad example there, PC.
But if they are still walking, the one ahead of the other will always be walking a greater distance than the other.
QUOTE (Bloy+May 23 2008, 12:57 PM)
But if they are still walking, the one ahead of the other will always be walking a greater distance than the other.
And therefore have nothing to do with this conversation as no infinity is involved with their walking.
And therefore have nothing to do with this conversation as no infinity is involved with their walking.
QUOTE (buttershug+May 23 2008, 07:16 AM)
And therefore have nothing to do with this conversation as no infinity is involved with their walking.
Okay, let me rephrase that...
If two walkers are walking an infinite distance, and one walker is ahead of the other walker, then the infinite walker ahead of the other infinite walker will always be walking an infinite distance that will be more than the infinite distance that the walker behind is infinitly walking.
Okay, let me rephrase that...
If two walkers are walking an infinite distance, and one walker is ahead of the other walker, then the infinite walker ahead of the other infinite walker will always be walking an infinite distance that will be more than the infinite distance that the walker behind is infinitly walking.
QUOTE (excaza+May 23 2008, 07:10 AM)
Well, if you say one infinity has more members than another infinity, wouldn't that make it finite?
I always did hate infinity and infinite series...
Not really.
The set of all numbers is infinite.
The set of positive numbers is infinite - even though there are obviously more numbers than there are positive numbers.
Positive numbers are an infinite subset of the larger infinite set.
I always did hate infinity and infinite series...
Not really.
The set of all numbers is infinite.
The set of positive numbers is infinite - even though there are obviously more numbers than there are positive numbers.
Positive numbers are an infinite subset of the larger infinite set.
QUOTE (Bloy+May 23 2008, 02:32 PM)
Okay, let me rephrase that...
If two walkers are walking an infinite distance, and one walker is ahead of the other walker, then the infinite walker ahead of the other infinite walker will always be walking an infinite distance that will be more than the infinite distance that the walker behind is infinitly walking.
If they are still walking then they havn't gone an infinite distance yet.
If two walkers are walking an infinite distance, and one walker is ahead of the other walker, then the infinite walker ahead of the other infinite walker will always be walking an infinite distance that will be more than the infinite distance that the walker behind is infinitly walking.
If they are still walking then they havn't gone an infinite distance yet.
QUOTE (gmilam+May 23 2008, 02:44 PM)
Not really.
The set of all numbers is infinite.
The set of positive numbers is infinite - even though there are obviously more numbers than there are positive numbers.
Positive numbers are an infinite subset of the larger infinite set.
not really.
Take natural numbers and integers.
Map 1 to 1
Map 2 to -1
Map 3 to 2
Map 4 to -2
And so on to infinity.
Both infinities are the same "size".
When talking about infinity if it's "obvious" it's probably wrong.
The set of all numbers is infinite.
The set of positive numbers is infinite - even though there are obviously more numbers than there are positive numbers.
Positive numbers are an infinite subset of the larger infinite set.
not really.
Take natural numbers and integers.
Map 1 to 1
Map 2 to -1
Map 3 to 2
Map 4 to -2
And so on to infinity.
Both infinities are the same "size".
When talking about infinity if it's "obvious" it's probably wrong.
QUOTE (buttershug+May 23 2008, 09:23 AM)
If they are still walking then they havn't gone an infinite distance yet.
let me call you on the term "yet".
just what do you mean when you say "yet"?
Are you implying that they will eventually reach infinity? To be AT infinity?
If so, tell me WHEN they will be AT infinity...since your "yet" adds the conditional aspect that they will eventually reach that distance.
note: Capitalized words are only for emphasis purposes.
let me call you on the term "yet".
just what do you mean when you say "yet"?
Are you implying that they will eventually reach infinity? To be AT infinity?
If so, tell me WHEN they will be AT infinity...since your "yet" adds the conditional aspect that they will eventually reach that distance.
note: Capitalized words are only for emphasis purposes.
QUOTE (Bloy+May 23 2008, 03:38 PM)
let me call you on the term "yet".
just what do you mean when you say "yet"?
Are you implying that they will eventually reach infinity? To be AT infinity?
If so, tell me WHEN they will be AT infinity...since your "yet" adds the conditional aspect that they will eventually reach that distance.
note: Capitalized words are only for emphasis purposes.
You can't get there from here.
Ok change that "yet" to "yet, and will only after an infinite amount of time aka never."
If they are walking then infinity doesn't enter into except maybe in their futile plans.
just what do you mean when you say "yet"?
Are you implying that they will eventually reach infinity? To be AT infinity?
If so, tell me WHEN they will be AT infinity...since your "yet" adds the conditional aspect that they will eventually reach that distance.
note: Capitalized words are only for emphasis purposes.
You can't get there from here.
Ok change that "yet" to "yet, and will only after an infinite amount of time aka never."
If they are walking then infinity doesn't enter into except maybe in their futile plans.
QUOTE (buttershug+May 23 2008, 10:29 AM)
not really.
Take natural numbers and integers.
Map 1 to 1
Map 2 to -1
Map 3 to 2
Map 4 to -2
And so on to infinity.
Both infinities are the same "size".
When talking about infinity if it's "obvious" it's probably wrong.
Well for every positive number there is a negative number.
Both are infinite and they do not intersect, yet both are contained in the set of all numbers.
And in answer to excaza's question - neither one becomes finite simply by being included in a different infinity.
Take natural numbers and integers.
Map 1 to 1
Map 2 to -1
Map 3 to 2
Map 4 to -2
And so on to infinity.
Both infinities are the same "size".
When talking about infinity if it's "obvious" it's probably wrong.
Well for every positive number there is a negative number.
Both are infinite and they do not intersect, yet both are contained in the set of all numbers.
And in answer to excaza's question - neither one becomes finite simply by being included in a different infinity.
QUOTE (buttershug+May 23 2008, 09:44 AM)
You can't get there from here.
Ok change that "yet" to "yet, and will only after an infinite amount of time aka never."
If they are walking then infinity doesn't enter into except maybe in their futile plans.
Yes, according to you their plans are to walk to infinity.
You have all along said that you can be AT infinity... so their plans are to walk and BE at infinity...and that is just what they are doing. Nothing more. They will never be AT infinity.
Now, for pure math purposes, you can fantasize being AT infinity and derive imaginative conclusions, but there is still the problem that it will never reflect physical reality.
Ok change that "yet" to "yet, and will only after an infinite amount of time aka never."
If they are walking then infinity doesn't enter into except maybe in their futile plans.
Yes, according to you their plans are to walk to infinity.
You have all along said that you can be AT infinity... so their plans are to walk and BE at infinity...and that is just what they are doing. Nothing more. They will never be AT infinity.
Now, for pure math purposes, you can fantasize being AT infinity and derive imaginative conclusions, but there is still the problem that it will never reflect physical reality.
QUOTE (gmilam+May 23 2008, 03:52 PM)
Well for every positive number there is a negative number.
Both are infinite and they do not intersect, yet both are contained in the set of all numbers.
And both are infinite and can't be size compared exclusivly the way you want to.
Both are infinite and they do not intersect, yet both are contained in the set of all numbers.
And both are infinite and can't be size compared exclusivly the way you want to.
QUOTE (Bloy+May 23 2008, 03:54 PM)
Yes, according to you their plans are to walk to infinity.
You have all along said that you can be AT infinity... so their plans are to walk and BE at infinity...and that is just what they are doing. Nothing more. They will never be AT infinity.
Now, for pure math purposes, you can fantasize being AT infinity and derive imaginative conclusions, but there is still the problem that it will never reflect physical reality.
I'm also balding.
Wait a minute that is not relevent.
But then again infinity not reflecting physical reality is not relevent either.
Do you guys sign up for a Fine Arts program then try to remove all abstractions?
Or do you just do that with Math?
Do you complain that Van Gogh's work does not look like photographs?
You have all along said that you can be AT infinity... so their plans are to walk and BE at infinity...and that is just what they are doing. Nothing more. They will never be AT infinity.
Now, for pure math purposes, you can fantasize being AT infinity and derive imaginative conclusions, but there is still the problem that it will never reflect physical reality.
I'm also balding.
Wait a minute that is not relevent.
But then again infinity not reflecting physical reality is not relevent either.
Do you guys sign up for a Fine Arts program then try to remove all abstractions?
Or do you just do that with Math?
Do you complain that Van Gogh's work does not look like photographs?
QUOTE (buttershug+May 23 2008, 10:02 AM)
I'm also balding.
Wait a minute that is not relevent.
But then again infinity not reflecting physical reality is not relevent either.
Do you guys sign up for a Fine Arts program then try to remove all abstractions?
Or do you just do that with Math?
Do you complain that Van Gogh's work does not look like photographs?
Time for an emoticon....
Wait a minute that is not relevent.
But then again infinity not reflecting physical reality is not relevent either.
Do you guys sign up for a Fine Arts program then try to remove all abstractions?
Or do you just do that with Math?
Do you complain that Van Gogh's work does not look like photographs?
Time for an emoticon....
QUOTE (Condraz23+Mar 24 2006, 06:54 PM)
One question, is a circle with infinite diamater a square? I am guessing that the bigger a circle gets, the lesser the edge's curved. If so, then would a circle of infinite length would actually be a square? Or would it just be a line that goes no-where forever?
I'm puzzled because a friend of mine believes that the Universe is infinite.
just to get back to the original question in this thread....
A circle represents a wave. It is never at rest... it represents both the macro universe as always in motion and the microsmic vibration that never rests.
I'm puzzled because a friend of mine believes that the Universe is infinite.
just to get back to the original question in this thread....
A circle represents a wave. It is never at rest... it represents both the macro universe as always in motion and the microsmic vibration that never rests.
QUOTE (buttershug+May 23 2008, 10:56 AM)
And both are infinite and can't be size compared exclusivly the way you want to.
Actually I wasn't trying to size compare anything. I was just pointing out that an entire infinite set being included as part of a "different" set does not make the first set finite.
At the risk of being lambasted for being a "concept" kind of a guy, the problem is that infinity is not an amount - it's a concept.
Actually I wasn't trying to size compare anything. I was just pointing out that an entire infinite set being included as part of a "different" set does not make the first set finite.
At the risk of being lambasted for being a "concept" kind of a guy, the problem is that infinity is not an amount - it's a concept.
QUOTE (Bloy+May 23 2008, 04:13 PM)
A circle represents a wave.
Not in the slightest, the 'wave' is a transitional manifestation of inter-dimensional morphology .
Wrong predictably again, you certified cofffin-headed, bollock-brain.
Not in the slightest, the 'wave' is a transitional manifestation of inter-dimensional morphology .
Wrong predictably again, you certified cofffin-headed, bollock-brain.
QUOTE
If they are still walking then they haven't walked an infinite distance, have they?
Still treating infinity as some largest quantity I see. If infinity was a reachable destination (which it is not) then once reached they would stop walking but if they stop then they have only traveled a finite distance.
See the paradox that results in treating infinity as something that is reachable. What makes the example represent walking infinity is in the fact that there doesn't exist a finite distance between them and the starting point. As soon as a finite distance is obtained, they have moved on and a larger distance exists. Thus if the distance between them is not finite (because they are still moving) then the distance between them and the starting point is infinite.
Now this is only true because there is no end to the road. They will never stop walking. If there was an end that that would mean at some finite time they will get to a finite distance in which they stop.
However in case that is all too much for you I'll demonstrate another way.
Two people walking down a road that has no end (infinity long) where 1 person is ahead of the other. An infinite amount of time has passed. The two have now walked an infinite distance yet one is still ahead of the other and both are still walking because the road has no end to reach.
However you can't seem to grasp physical demonstration so let's keep it mathematical.
The set of naturals is an infinite set. Aleph_0.
The set of reals is also an infinite set but is not countable. Aleph_1
Aleph_0 < Aleph_1
So you have one infinite set larger than the other. That gives you infinity < infinity.
Also to further demonstrate that a circle with an infinite anything is impossible think of a piece of paper that has an infinite height and length. So there is no edge to the page. You can draw a circle of any finite size but you still can't draw one of infinite size. Where would you start to draw the circumference? You start drawing at the end of what is to be the diameter but a circle with an infinite circumference will have an infinite diameter and so there is no end to begin drawing the circumference.
This goes with any geometric shape. Once you give a dimension an infinite length, you no longer have a geometric shape.
QUOTE (Precursor562+May 23 2008, 05:19 PM)
Two people walking down a road that has no end (infinity long) where 1 person is ahead of the other. An infinite amount of time has passed. The two have now walked an infinite distance yet one is still ahead of the other and both are still walking because the road has no end to reach.
However you can't seem to grasp physical demonstration so let's keep it mathematical.
We do get the physical misrepresentation.
You do not get the Mathematical one.
There can be no "after" an infinite amount of time.
Who's treating it like a quantity now?
And you are the one talking about it being reachable.
You can't reach infinity.
It's like the speed of light, if you are not already going at C then you can never reach that speed.
However you can't seem to grasp physical demonstration so let's keep it mathematical.
We do get the physical misrepresentation.
You do not get the Mathematical one.
There can be no "after" an infinite amount of time.
Who's treating it like a quantity now?
And you are the one talking about it being reachable.
You can't reach infinity.
It's like the speed of light, if you are not already going at C then you can never reach that speed.
QUOTE
There can be no "after" an infinite amount of time.
Who's treating it like a quantity now?
Who's treating it like a quantity now?
Well you know, it seems to be the only thing you(s) misunderstand so I went with that.
QUOTE (->
| QUOTE |
| There can be no "after" an infinite amount of time. Who's treating it like a quantity now? |
Well you know, it seems to be the only thing you(s) misunderstand so I went with that.
And you are the one talking about it being reachable.
Oh is that so. Please quote me where I say that the two people reach the end of the road that is infinite in length. The only time I mention reaching an end to a road, I specified the road as being finite in length.
I also see you don't even make an attempt at explaining how it is I didn't get the mathematical one.
Will you deny that the cardinality of the set of naturals is Aleph_0 (countably infinite)?
Will you deny that the cardinality of the set of reals is Aleph_1 (not countably infinity)?
Or will you deny Aleph_0 < Aleph_1?
QUOTE (Precursor562+May 23 2008, 06:10 PM)
Well you know, it seems to be the only thing you(s) misunderstand so I went with that.
Oh is that so. Please quote me where I say that the two people reach the end of the road that is infinite in length. The only time I mention reaching an end to a road, I specified the road as being finite in length.
You said that they walked an infinite amount of time.
How did they reach that time unless infinity is reachable?
And why do you talk about post secondary stuff like Aleph when you can't grasp primary level stuff like infinity is not a quantity.
And you didn't give a mathematical explanation of anything relevent.
Then number of zeros in 1.000... 10.000... 0.999... and in 9.999... are all Aleph0.
So Aleph0<Aleph1 has nothing to do with anything.
And note it is countably infinite, not countable.
The paper and drawing a circle is back to physical.
QUOTE (Sec+May 23 2008, 11:19 AM)
Not in the slightest, the 'wave' is a transitional manifestation of inter-dimensional morphology .
care to elaborate?
care to elaborate?
QUOTE (Bloy+May 23 2008, 07:36 PM)
care to elaborate?
A wave; Now you see it, now you don't. Here it is, there it goes. It's shaped like this, it's shaped like that. buh-bye
A circle; There it is, unchanging. forever C/D=pi
Personally I would have liked an elaboration of the cofffin-headed, bullock brain part of his post. For instance how does one become certified as such?
A wave; Now you see it, now you don't. Here it is, there it goes. It's shaped like this, it's shaped like that. buh-bye
A circle; There it is, unchanging. forever C/D=pi
Personally I would have liked an elaboration of the cofffin-headed, bullock brain part of his post. For instance how does one become certified as such?
QUOTE (buttershug+May 23 2008, 01:57 PM)
A wave; Now you see it, now you don't. Here it is, there it goes. It's shaped like this, it's shaped like that. buh-bye
A circle; There it is, unchanging. forever C/D=pi
Personally I would have liked an elaboration of the cofffin-headed, bullock brain part of his post. For instance how does one become certified as such?
BS...
a circle is not THERE. We can only draw it. But pi, in its ever changing, never resolved, always different value represents a circle that has no definitive quantitiy. You can lay it out into sine, cosine, etc,,,but it is always oscillating.
It is an oscillation... regardless of what frequency, amplitude, or length you select.
Now math might need to make it a constant, but we all know that pi isn't a constant in the true sense of the word.
A circle is never complete. it is either larger, or smaller than the so-called diameter. It is a wave. As it grows larger, as the OP was wondering, it is at the same time changing its velocity within the "apparent" expansion velocity.
If it becomes a square, as the OP was suggesting, then there is some other forces acting upon that circle to transform its pattern. This would indicate that the universe is not THE universe as something greater is acting upon the "supposed" infinitely expanding circular perimeter.
..and so it goes for the infinitely decreasing circular perimeter....whether it be a cell, a molecule, an atom, or a particle as we know them today.
A circle; There it is, unchanging. forever C/D=pi
Personally I would have liked an elaboration of the cofffin-headed, bullock brain part of his post. For instance how does one become certified as such?
BS...
a circle is not THERE. We can only draw it. But pi, in its ever changing, never resolved, always different value represents a circle that has no definitive quantitiy. You can lay it out into sine, cosine, etc,,,but it is always oscillating.
It is an oscillation... regardless of what frequency, amplitude, or length you select.
Now math might need to make it a constant, but we all know that pi isn't a constant in the true sense of the word.
A circle is never complete. it is either larger, or smaller than the so-called diameter. It is a wave. As it grows larger, as the OP was wondering, it is at the same time changing its velocity within the "apparent" expansion velocity.
If it becomes a square, as the OP was suggesting, then there is some other forces acting upon that circle to transform its pattern. This would indicate that the universe is not THE universe as something greater is acting upon the "supposed" infinitely expanding circular perimeter.
..and so it goes for the infinitely decreasing circular perimeter....whether it be a cell, a molecule, an atom, or a particle as we know them today.
Wow, you people are really lost with the idea of Infinity!
'Infinite circle' is an oxymoron. Neither is there any such thing as 'Infinite distance', or even 'direction'. The moment you posit a 'second thing', you are not describing the necessarily Infinite. There can be no 'beginning', nor 'end', to anything considered to be 'Infinite'. The correct dictionary definition is used for the notion of 'without boundaries'.
So, only One truly Infinite thing can exist, and it must thus necessarily exist everwhere. 'Speed' does not apply, as you must posit the idea of at least two discrete 'points' in order for 'speed' to happen. Humans do this erroneously, when we describe the world around us without recognising that everything is interconnected.
Infinity = 1 ...because anything posited to be Infinite can only be One thing, in Reality. '1' is the only number that corresponds to 'non-divideable' (without boundaries), and '0' simply does not exist.
Every'thing' has an inherent element of 'infiniteness' about it...cause/effect - same thing; constantly changing.
What we currently interpret as the 'finite' physical universe, is the momentary appearance of Infinite Space, condensed into 'physicality' - all of these 'appearances' must return to the Infinite (true/pure) wave-state. This is why the 'black holes' at the centres of 'Galaxies' exist.
QUOTE
What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances). - Erwin Schrödinger
g.
I'm sorry, in my last post I said that math made pi a constant... or needed it to be... I was wrong.
QUOTE (Bloy+May 23 2008, 11:00 PM)
I'm sorry, in my last post I said that math made pi a constant... or needed it to be... I was wrong.
Some people say pi r squared.
But you and I know better cake are square, pie are round.
Some people say pi r squared.
But you and I know better cake are square, pie are round.
QUOTE
You said that they walked an infinite amount of time.
How did they reach that time unless infinity is reachable?
How did they reach that time unless infinity is reachable?
Yeah and I also said...
QUOTE (->
| QUOTE |
| You said that they walked an infinite amount of time. How did they reach that time unless infinity is reachable? |
Yeah and I also said...
Well you know, it seems to be the only thing you(s) misunderstand so I went with that.
QUOTE
Then number of zeros in 1.000... 10.000... 0.999... and in 9.999... are all Aleph0.
Do you know what aleph_0 and aleph_1 even means.
If the elements of an infinite set are countable (able to be put into a 1:1 with the whole numbers) then it is aleph_0. The first case in which the elements are not countable are aleph_1.
The natural number set is [1, 2, 3, .....] which can be counted...
1->0
2->1
3->2
etc.
The real number set is, well, good luck showing elements where one comes after the other. the best you can do is...
[......,4,....,3,.....,2,.....,1,.....,0,.....,-1,.....,-2,.....,-3,.....,-4,.....]
Between each integer exist an infinite number of decimal numbers. It is impossible to put the set into a 1:1. That is what makes it aleph_1.
Cardinality refers to the size of a set and so the set of reals is a larger set than the set of naturals. Both are infinite and so the result is different size infinities.
Oh and as for the numbers you gave. If the zeros in both 1.0000..... and 10.000.... are elements of a set then you have two infinite sets which are aleph_0.
0.999... only has one 0 so you don't have an infinite set.
9.999... has no 0's at all.
For Bloy's benefit, C = 2 Pi r is valid for any circle, the C and r will be different for every circle but the ratio C/r will always be 2 Pi.
I believe the below is worth reposting in its entirety...
From...
http://mathforum.org/library/drmath/view/55021.html
Date: 06/26/98 at 16:25:15
From: Doctor Barrus
Subject: Re: Is pi a constant in non-Euclidean geometry?
Hi, Sean!
Well, you're both right in different cases. Whenever you're talking
about perfect circles on flat (Euclidean) surfaces, then pi, which
represents the ratio of the circumference of the circle to its
diameter, is a constant. (By the way, this number is irrational but it
IS a constant, just as the square root of 2 is a single irrational
constant whose decimal expansion goes on forever. Take 1, 1.4, 1.41,
1.414, or any other approximation of the square root of 2 and square
it, and you won't get 2. Only the irrational square root of 2 squares
to 2. Similarly, there is only one number, pi, in all its irrational
glory, that represents the circle's ratio.)
However, if you go into NON-Euclidean geometry, where you deal with
curved surfaces, then the ratio of a circle's circumference to its
diameter does not remain constant. For example, say you stretched a
piece of rubber over a circular hoop. When the rubber lies flat,
you've got a flat (Euclidean) circle, and the ratio of the
circumference to the diameter is pi = 3.14159265358... But say you
poked your finger through the center of the circle and stretched the
rubber a bit. Then the diameter of the circle would grow, but the
circumference would be the same. The ratio would change - it wouldn't
be constant. Consequently, if you called this ratio pi, then pi
wouldn't be constant.
It gets a whole lot more complicated in non-Euclidan geometry than
this. For example, suppose you traced a circle (and you have to be
careful of your definition of circles in non-Euclidean geometry) on a
horse's saddle. This constitutes a surface with negative curvature.
The ratio of circumference to diameter is not easy to compute exactly
without advanced mathematics, let alone to describe!
So you see, you're right that pi is a constant when you're dealing
with Euclidean, or flat surfaces. However, your friends are right in
that the ratio of the circumference of a circle to its diameter
changes and is not constant in non-Euclidean spaces.
Whew! Long answer, but I hope it's helped.
- Doctor Barrus, The Math Forum
From...
http://mathforum.org/library/drmath/view/55021.html
Date: 06/26/98 at 16:25:15
From: Doctor Barrus
Subject: Re: Is pi a constant in non-Euclidean geometry?
Hi, Sean!
Well, you're both right in different cases. Whenever you're talking
about perfect circles on flat (Euclidean) surfaces, then pi, which
represents the ratio of the circumference of the circle to its
diameter, is a constant. (By the way, this number is irrational but it
IS a constant, just as the square root of 2 is a single irrational
constant whose decimal expansion goes on forever. Take 1, 1.4, 1.41,
1.414, or any other approximation of the square root of 2 and square
it, and you won't get 2. Only the irrational square root of 2 squares
to 2. Similarly, there is only one number, pi, in all its irrational
glory, that represents the circle's ratio.)
However, if you go into NON-Euclidean geometry, where you deal with
curved surfaces, then the ratio of a circle's circumference to its
diameter does not remain constant. For example, say you stretched a
piece of rubber over a circular hoop. When the rubber lies flat,
you've got a flat (Euclidean) circle, and the ratio of the
circumference to the diameter is pi = 3.14159265358... But say you
poked your finger through the center of the circle and stretched the
rubber a bit. Then the diameter of the circle would grow, but the
circumference would be the same. The ratio would change - it wouldn't
be constant. Consequently, if you called this ratio pi, then pi
wouldn't be constant.
It gets a whole lot more complicated in non-Euclidan geometry than
this. For example, suppose you traced a circle (and you have to be
careful of your definition of circles in non-Euclidean geometry) on a
horse's saddle. This constitutes a surface with negative curvature.
The ratio of circumference to diameter is not easy to compute exactly
without advanced mathematics, let alone to describe!
So you see, you're right that pi is a constant when you're dealing
with Euclidean, or flat surfaces. However, your friends are right in
that the ratio of the circumference of a circle to its diameter
changes and is not constant in non-Euclidean spaces.
Whew! Long answer, but I hope it's helped.
- Doctor Barrus, The Math Forum
I don't think we're talking about non Euclidean geometry - no one other than you has mentioned curved spaces. Interesting post though.
Regardless of the possibility of different infinities and regardless of the different ratio. The circumference of a circle exists at the edge of its diameter. A circle with any of its variables infinite will result in all of its variables infinite including the diameter.
If the diameter is infinite then there is no edge for the circumference to exist. You simply don't have a circle.
If the diameter is infinite then there is no edge for the circumference to exist. You simply don't have a circle.
QUOTE (Precursor562+May 24 2008, 02:08 AM)
Oh and as for the numbers you gave. If the zeros in both 1.0000..... and 10.000.... are elements of a set then you have two infinite sets which are aleph_0.
0.999... only has one 0 so you don't have an infinite set.
9.999... has no 0's at all.
I meant the 9's in 0.999...
and 9.999...
But I see you say that the 0's in 1.000... and 10.000... are both aleph_0.
Would say the same is true for the 9's in 0.999... and 9.999...?
If so then why does that proof not work for 0.999... =1.000...?
In the other thread you claimed the proof given in Wiki is not valid.
If the 9's in 0.999... and 9.999... are both aleph_0 then whywould that proof not be valid.
Yours and StevenA's claim for it not being valid was based on the 9's being different but you agree they are both aleph_0.
0.999... only has one 0 so you don't have an infinite set.
9.999... has no 0's at all.
I meant the 9's in 0.999...
and 9.999...
But I see you say that the 0's in 1.000... and 10.000... are both aleph_0.
Would say the same is true for the 9's in 0.999... and 9.999...?
If so then why does that proof not work for 0.999... =1.000...?
In the other thread you claimed the proof given in Wiki is not valid.
If the 9's in 0.999... and 9.999... are both aleph_0 then whywould that proof not be valid.
Yours and StevenA's claim for it not being valid was based on the 9's being different but you agree they are both aleph_0.
Not sure what you're talking about. Are you talking about where multiplying by 10 and adding 9 can potentially result in different .9r's?
Such has nothing to do with cardinality if that is the case. It has to do with that if the terms (not digits of the numbers) involved were put into a set, you don't get identical sets because each one has a different ordinal.
There are three criteria for two sets to be identical.
Same elements
Same ordinal
Same cardinal
In that case, 1.000... = 2.000... because both have aleph_0 0's.
Such has nothing to do with cardinality if that is the case. It has to do with that if the terms (not digits of the numbers) involved were put into a set, you don't get identical sets because each one has a different ordinal.
There are three criteria for two sets to be identical.
Same elements
Same ordinal
Same cardinal
QUOTE
If so then why does that proof not work for 0.999... =1.000...?
In that case, 1.000... = 2.000... because both have aleph_0 0's.
QUOTE (Precursor562+May 24 2008, 01:56 PM)
Not sure what you're talking about. Are you talking about where multiplying by 10 and adding 9 can potentially result in different .9r's?
Such has nothing to do with cardinality if that is the case. It has to do with that if the terms (not digits of the numbers) involved were put into a set, you don't get identical sets because each one has a different ordinal.
There are three criteria for two sets to be identical.
Same elements
Same ordinal
Same cardinal
In that case, 1.000... = 2.000... because both have aleph_0 0's.
You really do like to twist things around
I was talking about this proof.
Which doesn't require sets.
C=0.999…
10C=9.999…
10C-C=9.999…-0.999…
9C=9
C=1
0.999…=1
And there is no mention of sets. you can do every step above because 9.999... is ten times bigger than 0.999...
0.999... is the same in both 0.999... and 9.999...
there is the same non-specific, aleph_0 infinity quanity of 9's in both cases.
And you make such crazy leaps
the .000... in both 1.000... and 2.000... are identical because both have aleph_0 0's. But that does not make the 1 and the 2 identical.
O HEY did you notice you said "becase both have aleph_0 0's" without that construction nonsense, that you and StevenA seem to insist on? You quite correctly said it without any such conditions.
Such has nothing to do with cardinality if that is the case. It has to do with that if the terms (not digits of the numbers) involved were put into a set, you don't get identical sets because each one has a different ordinal.
There are three criteria for two sets to be identical.
Same elements
Same ordinal
Same cardinal
In that case, 1.000... = 2.000... because both have aleph_0 0's.
You really do like to twist things around
I was talking about this proof.
Which doesn't require sets.
C=0.999…
10C=9.999…
10C-C=9.999…-0.999…
9C=9
C=1
0.999…=1
And there is no mention of sets. you can do every step above because 9.999... is ten times bigger than 0.999...
0.999... is the same in both 0.999... and 9.999...
there is the same non-specific, aleph_0 infinity quanity of 9's in both cases.
And you make such crazy leaps
the .000... in both 1.000... and 2.000... are identical because both have aleph_0 0's. But that does not make the 1 and the 2 identical.
O HEY did you notice you said "becase both have aleph_0 0's" without that construction nonsense, that you and StevenA seem to insist on? You quite correctly said it without any such conditions.
.9r = .9 + .09 + .009 +.....
Put each term into a set and you get an infinite set...
[.9, .09, .009, ......]
Cardinal of Aleph_0
Ordinal of ω
where .9r = x then 10x is 9.9r but when applied to the above you have...
10(.9r) = 10(.9 + .09 + .009 +.....)
This results in....
9.9r = 9 + .9 + .09 +.....
You are taking each term (element of the set) and multiplying it by 10.
It maintains the same cardinal and the same ordinal.
So you get [9, .9, .09, ....] with cardinal aleph_0 and ordinal ω.
But something different happens when you simply add 9.
.9r + 9 = .9 + .09 + .009 +.... + 9
9.9r = 9 + .9 + .09 + .009.
How is this different?
Because [.9, .09, .009, ....] * [10] != [.9, .09, .009, ....] + [9]
[.9, .09, .009, ....] * [10] = [.9(10), .09(10), .009(10), .....] = [9, .9, .09, ....]
Ordinal ω
[.9, .09, .009, ....] + [9] = [.9, .09, .009, ...., 9] = [9, .9, .09, .009, ....]
Ordinal ω+1
In order for the two sets to be identical you need...
Identical elements (which we have)
Identical cardinal (which we have)
Identical ordinal (which we don't have)
ω != ω+1 and so...
[9, .9, .09, .009, ....] != [9, .9, .09, .009, ....]
Since each element is a term within a summation....
9 + .9 + .09 + .009 +.... != 9 + .9 + .09 + .009 +.....
9.9r != 9.9r
Where one 9.9r is .9r *10 and the other is .9r + 9 then it means...
.9r * 10 != .9r + 9
See I tried to show this with finite length decimals since the problem was with the fact that the decimal is infinite. Except I always get "just because it works for the finite doesn't mean it works with the infinite" and although a true statement, mathematical induction demonstrates that this is a case where what works for the finite also works for the infinite.
.999 * 10 = 9.99
.999 + 9 = 9.999
9.99 != 9.999
Now having the 9's after the decimal infinite hides this occurrence but the existence of unequal infinity allows such an occurrence that works with the finite to also work with the infinite.
Put each term into a set and you get an infinite set...
[.9, .09, .009, ......]
Cardinal of Aleph_0
Ordinal of ω
where .9r = x then 10x is 9.9r but when applied to the above you have...
10(.9r) = 10(.9 + .09 + .009 +.....)
This results in....
9.9r = 9 + .9 + .09 +.....
You are taking each term (element of the set) and multiplying it by 10.
It maintains the same cardinal and the same ordinal.
So you get [9, .9, .09, ....] with cardinal aleph_0 and ordinal ω.
But something different happens when you simply add 9.
.9r + 9 = .9 + .09 + .009 +.... + 9
9.9r = 9 + .9 + .09 + .009.
How is this different?
Because [.9, .09, .009, ....] * [10] != [.9, .09, .009, ....] + [9]
[.9, .09, .009, ....] * [10] = [.9(10), .09(10), .009(10), .....] = [9, .9, .09, ....]
Ordinal ω
[.9, .09, .009, ....] + [9] = [.9, .09, .009, ...., 9] = [9, .9, .09, .009, ....]
Ordinal ω+1
In order for the two sets to be identical you need...
Identical elements (which we have)
Identical cardinal (which we have)
Identical ordinal (which we don't have)
ω != ω+1 and so...
[9, .9, .09, .009, ....] != [9, .9, .09, .009, ....]
Since each element is a term within a summation....
9 + .9 + .09 + .009 +.... != 9 + .9 + .09 + .009 +.....
9.9r != 9.9r
Where one 9.9r is .9r *10 and the other is .9r + 9 then it means...
.9r * 10 != .9r + 9
See I tried to show this with finite length decimals since the problem was with the fact that the decimal is infinite. Except I always get "just because it works for the finite doesn't mean it works with the infinite" and although a true statement, mathematical induction demonstrates that this is a case where what works for the finite also works for the infinite.
.999 * 10 = 9.99
.999 + 9 = 9.999
9.99 != 9.999
Now having the 9's after the decimal infinite hides this occurrence but the existence of unequal infinity allows such an occurrence that works with the finite to also work with the infinite.
QUOTE (Precursor562+May 24 2008, 02:52 PM)
.9r = .9 + .09 + .009 +.....
And you start off irrelevent.
And then keep getting more and irrrelevent.
And you start off irrelevent.
And then keep getting more and irrrelevent.
QUOTE (buttershug+May 24 2008, 09:00 AM)
And you start off irrelevent.
And then keep getting more and irrrelevent.
If something is irrelevent, can it be MORE irrelevent?
And then keep getting more and irrrelevent.
If something is irrelevent, can it be MORE irrelevent?
<edit> [deleted]
QUOTE (Precursor562+May 24 2008, 02:52 PM)
.But something different happens when you simply add 9.
Where is the adding 9 in the proof in my post?
1:C=0.999…
2:10C=9.999…
3:10C-C=9.999…-0.999…
4:9C=9
5:C=1
6:0.999…=1
which of those 6 lines involves adding 9 to anything?
And what unequal infinity?
Where is the adding 9 in the proof in my post?
1:C=0.999…
2:10C=9.999…
3:10C-C=9.999…-0.999…
4:9C=9
5:C=1
6:0.999…=1
which of those 6 lines involves adding 9 to anything?
And what unequal infinity?
You multiply .999... by 10 to get 9.99... then you subtract .999... to get 9 treating the .99... as if it is the same as the .999... you started with. The only way to get 9.999... where the .999... is the one you started with is if you add 9 to it. Showing that the .9r's are not the same between the multiply by 10 and add 9 will show that .9r is not equal to 1 since taking 1 and multiplying by 10 or adding 9 will result in the same number.
If you have to ask then clearly you don't know this stuff to the slightest degree.
The number of digits.
.999.... = .9 + .09 + .009 +....
Multiply by ten and all you do is multiply each term by 10. This keeps the ordinal the same.
Add 9 and you don't do anything to each term. You add an additional term to the existing ones. This changes the ordinal.
So placed as elements of a set you don't have identical sets. Just because you fail to see the relevance doesn't make it irrelevant.
The proof is very simple.
.9r = .9 + .09 + .009 + .....
That means instead of using .999... we can use .9 + .09 + .009 +.....
We can use each term as an element of a set (don't have to but it makes it easier to see the difference).
[10] * [.9, .09, .009, ....] != [9] + [.9, .09, .009, ....]
The result is non identical sets. Which means when each element is used as a term within a summation results in non identical sums.
Now you can say the same with 1 where 1 = 1 + .0 + .00 + .000 +....
Such that [10] * [1, .0, .00, .000, ...] != [9] + [1, .0, .00, .000, ...]
That is you don't get identical sets. In this case you don't have to and the reason is in the zeros.
1.0 = 1.00 = 1.000 = 1.0000 etc.
but
9.9 != 9.99 != 9.999 != 9.9999 etc.
So although, with the set that equals 1, adding 9 and multiplying by 10 will not give identical sets, used as terms will give an identical number because of the irrelevance of the quantity of zeros after the decimal.
QUOTE
And what unequal infinity?
If you have to ask then clearly you don't know this stuff to the slightest degree.
The number of digits.
.999.... = .9 + .09 + .009 +....
Multiply by ten and all you do is multiply each term by 10. This keeps the ordinal the same.
Add 9 and you don't do anything to each term. You add an additional term to the existing ones. This changes the ordinal.
So placed as elements of a set you don't have identical sets. Just because you fail to see the relevance doesn't make it irrelevant.
The proof is very simple.
.9r = .9 + .09 + .009 + .....
That means instead of using .999... we can use .9 + .09 + .009 +.....
We can use each term as an element of a set (don't have to but it makes it easier to see the difference).
[10] * [.9, .09, .009, ....] != [9] + [.9, .09, .009, ....]
The result is non identical sets. Which means when each element is used as a term within a summation results in non identical sums.
Now you can say the same with 1 where 1 = 1 + .0 + .00 + .000 +....
Such that [10] * [1, .0, .00, .000, ...] != [9] + [1, .0, .00, .000, ...]
That is you don't get identical sets. In this case you don't have to and the reason is in the zeros.
1.0 = 1.00 = 1.000 = 1.0000 etc.
but
9.9 != 9.99 != 9.999 != 9.9999 etc.
So although, with the set that equals 1, adding 9 and multiplying by 10 will not give identical sets, used as terms will give an identical number because of the irrelevance of the quantity of zeros after the decimal.
QUOTE (Precursor562+May 25 2008, 03:17 PM)
You multiply .999... by 10 to get 9.99... then you subtract .999... to get 9 treating the .99... as if it is the same as the .999... you started with. The only way to get 9.999... where the .999... is the one you started with is if you add 9 to it.
No it isn't you can simply multiply by ten.
And both .999...'s are the same,
No need to add 9.
Why is it the 0.999...!=1 people have to complicate simple proofs?
And someone agreed it had the same aleph_0 and cardinality to it.
O hey wait a minute that was you!!!!!!!!!!
No it isn't you can simply multiply by ten.
And both .999...'s are the same,
No need to add 9.
Why is it the 0.999...!=1 people have to complicate simple proofs?
And someone agreed it had the same aleph_0 and cardinality to it.
O hey wait a minute that was you!!!!!!!!!!
QUOTE
No it isn't you can simply multiply by ten.
The whole point of treating the terms as elements of a set and demonstrating that you don't get identical sets proves that you can't simply multiply by ten.
QUOTE (->
| QUOTE |
| No it isn't you can simply multiply by ten. |
The whole point of treating the terms as elements of a set and demonstrating that you don't get identical sets proves that you can't simply multiply by ten.
And both .999...'s are the same,
The fact that you don't get identical sets using summation terms as the elements of said sets proves that the sum you get from each is not an identical sum. They are then not equal. Not the same.
QUOTE
Why is it the 0.999...!=1 people have to complicate simple proofs?
There exists another simple proof. It proves 1 = 2.
QUOTE (->
| QUOTE |
| Why is it the 0.999...!=1 people have to complicate simple proofs? |
There exists another simple proof. It proves 1 = 2.
And someone agreed it had the same aleph_0 and cardinality to it.
Your point? It's called different ordinals.
Say it with me now...
o-r-d-i-n-a-l-s.
Identical sets with have...
1. The same elements
2. The same cardinality
3. The same ordinal
Oh and since you brought this whole thing up. How does it relate to an infinite circle? Let's try keeping the .9r talk in the .9r thread.
If it was truly infinite, wouldn't it lose what makes it a "circle" and just be a plane?
QUOTE (excaza+May 27 2008, 11:50 AM)
If it was truly infinite, wouldn't it lose what makes it a "circle" and just be a plane?
No, a sphere.
g.
No, a sphere.
g.
QUOTE
If it was truly infinite, wouldn't it lose what makes it a "circle" and just be a plane?
Exactly.
QUOTE (Gorgeous+May 27 2008, 12:14 PM)
No, a sphere.
g.
...because Infinite Space is truly 3-dimensional.
g.
g.
...because Infinite Space is truly 3-dimensional.
g.
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