One is the whole. the whole of everything or something or nothing. This may sound like a syntax issue except in the grand picture.
QUOTE (Amiga-x+Jan 6 2008, 12:14 AM)
One is the whole. the whole of everything or something or nothing. This may sound like a syntax issue except in the grand picture.
You're trying to treat variables as numbers, by which I mean, for instance, that x/x = 1 holds true, but simply plugging in x=0 and then saying 0/0 = 1 isn't. The same thing holds true for infinity, which is not a number, but a concept. I'll just briefly mention limits and L'Hopital's rule; unfortunately, I do not have the time to go into detail as my presence is required elsewhere. I will attempt to get back to this at a later time, if possible.
You're trying to treat variables as numbers, by which I mean, for instance, that x/x = 1 holds true, but simply plugging in x=0 and then saying 0/0 = 1 isn't. The same thing holds true for infinity, which is not a number, but a concept. I'll just briefly mention limits and L'Hopital's rule; unfortunately, I do not have the time to go into detail as my presence is required elsewhere. I will attempt to get back to this at a later time, if possible.
There is not much that I remember from my high school math courses after more than 20 years, but I remember the teacher saying that one can never divide anything by a zero. It is a "Thou shalt not...."
in that line of thought:1/1=0
if You stay within one scale, 0/0 is any finite value.
The rule of LHopital says in essence if 0/0 = f(x)/g(x) at one scale, but we can downscale it by differentiation so that at some scale g(x) is not 0, than we will recover that finite value, and the scale where these 2 functions at that point have finite values.
If however, all differentials of f(x) , g(x) is also 0 at xo, than downscaling does not help to find that finite value.
The rule of LHopital says in essence if 0/0 = f(x)/g(x) at one scale, but we can downscale it by differentiation so that at some scale g(x) is not 0, than we will recover that finite value, and the scale where these 2 functions at that point have finite values.
If however, all differentials of f(x) , g(x) is also 0 at xo, than downscaling does not help to find that finite value.
0/0= -00
QUOTE (NeoNo.1+Jan 6 2008, 09:47 AM)
0/0= -00
Neo, I'm not sure if you mean -00 to be negative infinity or something made up.
On topic, I was going to elaborate on my earlier post, but I feel Ivars post to be "acceptable."
Neo, I'm not sure if you mean -00 to be negative infinity or something made up.
On topic, I was going to elaborate on my earlier post, but I feel Ivars post to be "acceptable."
QUOTE (Amiga-x+)
One is the whole. the whole of everything or something or nothing. This may sound like a syntax issue except in the grand picture.
Technically division by 0 isn't defined, but depending upon the context of the zeroes involved, there are times when such an identity could prove useful to assume true.
Ideally 0/0 should be equal to 1. The issue though is that how a zero was derived isn't always clear and in that case you can't determine which class/type of zero someone is referring to because the natural assumption is that having zero of something is the same as having nothing at all, which isn't always a useful way to look at it and it would likely be better to say that, for example, 0x=0x, but that 0x!=0, depending upon what types of zeroes are being used (in a sense, just like not all infinities are necessarily equal).
But I'd agree that without all these unstated contexts, 0/0 should be equal to 1 and infinity/infinity should be equal to 1 and infinity-infinity should be equal to 0 also, but I don't know of a mathematical system that's available that's general purpose enough to be able to assure these identities would always be true (and probably a better system is needed, though there could be systems of a more set theoretical kind that could work in this manner).
Technically division by 0 isn't defined, but depending upon the context of the zeroes involved, there are times when such an identity could prove useful to assume true.
Ideally 0/0 should be equal to 1. The issue though is that how a zero was derived isn't always clear and in that case you can't determine which class/type of zero someone is referring to because the natural assumption is that having zero of something is the same as having nothing at all, which isn't always a useful way to look at it and it would likely be better to say that, for example, 0x=0x, but that 0x!=0, depending upon what types of zeroes are being used (in a sense, just like not all infinities are necessarily equal).
But I'd agree that without all these unstated contexts, 0/0 should be equal to 1 and infinity/infinity should be equal to 1 and infinity-infinity should be equal to 0 also, but I don't know of a mathematical system that's available that's general purpose enough to be able to assure these identities would always be true (and probably a better system is needed, though there could be systems of a more set theoretical kind that could work in this manner).
QUOTE (Guest00+Jan 6 2008, 10:12 AM)
Neo, I'm not sure if you mean -00 to be negative infinity or something made up.
On topic, I was going to elaborate on my earlier post, but I feel Ivars post to be "acceptable."
Hello???????
Ever heard of Rotational Values?
On topic, I was going to elaborate on my earlier post, but I feel Ivars post to be "acceptable."
Hello???????
Ever heard of Rotational Values?
QUOTE (StevenA+Jan 6 2008, 12:40 PM)
Ideally 0/0 should be equal to 1.
Why? I can always give an example which limits to 0/0 but which limits to a value which isn't 1.
sin(kx)/x limits to k as x->0 for instance.
Why? I can always give an example which limits to 0/0 but which limits to a value which isn't 1.
sin(kx)/x limits to k as x->0 for instance.
QUOTE (StevenA+Jan 6 2008, 12:40 PM)
nd it would likely be better to say that, for example, 0x=0x, but that 0x!=0, depending upon what types of zeroes are being used (in a sense, just like not all infinities are necessarily equal).
Unlike infinity, where you can consistently define different notions of it (in terms of cardinality), zero is zero. It's provable that if you assume the existence of two or more zeros within the Reals (or indeed any group, ring or field) then all you've done is just relabel the one and only one zero. 'A rose by any other name'
QUOTE (StevenA+Jan 6 2008, 12:40 PM)
0/0 should be equal to 1 and infinity/infinity should be equal to 1 and infinity-infinity should be equal to 0 also
In all those cases I can construct counter examples using limits.
sin(kx)/x as x->0 goes to k, not 1
(x+1)/x^2 -> 0 as x->infinity
(x^3+1)/x^2-1 -> infinity as x->infinity
(kx^2 + x)/x^2 -> k as x->infinity
(x^2+1)/(x+1) - x -> 0 as x->infinity
(x^2+1)/(x+1) - 2x -> -infinity as x->infinity
(x^2+1)/(x+1) + (1-x) -> 1 as x->infinity
You really do need to learn about limits.
sin(kx)/x as x->0 goes to k, not 1
(x+1)/x^2 -> 0 as x->infinity
(x^3+1)/x^2-1 -> infinity as x->infinity
(kx^2 + x)/x^2 -> k as x->infinity
(x^2+1)/(x+1) - x -> 0 as x->infinity
(x^2+1)/(x+1) - 2x -> -infinity as x->infinity
(x^2+1)/(x+1) + (1-x) -> 1 as x->infinity
You really do need to learn about limits.
QUOTE (StevenA+Jan 6 2008, 12:40 PM)
but I don't know of a mathematical system that's
You don't know about results found in high school textbooks taught to children, so there's no suprise.
Cool, I never thought about it that way.
If we make what I owe the IRS x and what the IRS receives is x than:
x= x
Since no one can argue with math and it is legal to multiply both sides of an equation with the same thing and still be equal.
0 (x) = 0 (x)
I guess I can just send that in and we are square every year.
If we make what I owe the IRS x and what the IRS receives is x than:
x= x
Since no one can argue with math and it is legal to multiply both sides of an equation with the same thing and still be equal.
0 (x) = 0 (x)
I guess I can just send that in and we are square every year.
QUOTE (4Dguy+Jan 7 2008, 05:15 PM)
Cool, I never thought about it that way.
If we make what I owe the IRS x and what the IRS receives is x than:
x= x
Since no one can argue with math and it is legal to multiply both sides of an equation with the same thing and still be equal.
0 (x) = 0 (x)
I guess I can just send that in and we are square every year.
Here's something easier...
0 (x) = 0 (x) >-< 0 (x') = 0 (x')
If we make what I owe the IRS x and what the IRS receives is x than:
x= x
Since no one can argue with math and it is legal to multiply both sides of an equation with the same thing and still be equal.
0 (x) = 0 (x)
I guess I can just send that in and we are square every year.
Here's something easier...
0 (x) = 0 (x) >-< 0 (x') = 0 (x')
NeoNo.1
c/c=1 in every frame but not the same thing in relativity.
c/c=1 in every frame but not the same thing in relativity.
QUOTE (4Dguy+Jan 7 2008, 01:15 PM)
Cool, I never thought about it that way.
If we make what I owe the IRS x and what the IRS receives is x than:
x= x
Since no one can argue with math and it is legal to multiply both sides of an equation with the same thing and still be equal.
0 (x) = 0 (x)
I guess I can just send that in and we are square every year.
If we make what I owe the IRS x and what the IRS receives is x than:
x= x
Since no one can argue with math and it is legal to multiply both sides of an equation with the same thing and still be equal.
0 (x) = 0 (x)
I guess I can just send that in and we are square every year.
QUOTE (AlphaNumeric+Jan 6 2008, 08:11 PM)
Why? I can always give an example which limits to 0/0 but which limits to a value which isn't 1.
sin(kx)/x limits to k as x->0 for instance.
Unlike infinity, where you can consistently define different notions of it (in terms of cardinality), zero is zero. It's provable that if you assume the existence of two or more zeros within the Reals (or indeed any group, ring or field) then all you've done is just relabel the one and only one zero. 'A rose by any other name'
In all those cases I can construct counter examples using limits.
sin(kx)/x as x->0 goes to k, not 1
(x+1)/x^2 -> 0 as x->infinity
(x^3+1)/x^2-1 -> infinity as x->infinity
(kx^2 + x)/x^2 -> k as x->infinity
(x^2+1)/(x+1) - x -> 0 as x->infinity
(x^2+1)/(x+1) - 2x -> -infinity as x->infinity
(x^2+1)/(x+1) + (1-x) -> 1 as x->infinity
You really do need to learn about limits.
You don't know about results found in high school textbooks taught to children, so there's no suprise.
Notice that in all your limit examples, you are working with sets though and not simply 0 and this is why with such a system of mathematics, 0/0 can't be defined as 1, though if we had a more deterministic manner to construct a multiplication by an infinite process, then it would potentially become possible to deterministically define its representation instead as a division by 0.
I think constructing such a deterministic system, in which a division by 0 was defineable and had a deterministic result would be an advantage though. The question would be over the tradeoffs that would need to be made elsewhere in order to allow for this and it may not be useful enough to be applied in general (though I think by maintaining a record of which dimension the zero was constructed, the indeterminism of having all zeroes equal to each other could be removed and we would be able to linearly correlate between zeroes in multiple dimensions).
For example, if we multiply a inch by 2 we have 2 inches, but if we multiply an inch by zero we shouldn't get an unadulterated 0 but instead 0 inches. So a multiplication of a variable x by 0 should create 0x and not 0. Normal this isn't an issue when the constant coefficient is non-zero because x can vary and the resulting variation in the scaling is not ignorable and a linear relationship to x is specified, but when we define a multiplication by 0 to construct a non-descript 0 then for multiplication, this isn't sufficiently deterministics as it destroys linear information and hence we can't later compute an inverse and divide by 0, but if the information was retained, then we could invert a multiplication by zero and reconstruct the input (which happens to be necessary for many proofs, even if the end results are the same, they aren't provable correct and can degrade unless the influence of every input to every output is determinable).
As a matter of fact, I should post a thread on some ideas regarding this.
sin(kx)/x limits to k as x->0 for instance.
Unlike infinity, where you can consistently define different notions of it (in terms of cardinality), zero is zero. It's provable that if you assume the existence of two or more zeros within the Reals (or indeed any group, ring or field) then all you've done is just relabel the one and only one zero. 'A rose by any other name'
In all those cases I can construct counter examples using limits.
sin(kx)/x as x->0 goes to k, not 1
(x+1)/x^2 -> 0 as x->infinity
(x^3+1)/x^2-1 -> infinity as x->infinity
(kx^2 + x)/x^2 -> k as x->infinity
(x^2+1)/(x+1) - x -> 0 as x->infinity
(x^2+1)/(x+1) - 2x -> -infinity as x->infinity
(x^2+1)/(x+1) + (1-x) -> 1 as x->infinity
You really do need to learn about limits.
You don't know about results found in high school textbooks taught to children, so there's no suprise.
Notice that in all your limit examples, you are working with sets though and not simply 0 and this is why with such a system of mathematics, 0/0 can't be defined as 1, though if we had a more deterministic manner to construct a multiplication by an infinite process, then it would potentially become possible to deterministically define its representation instead as a division by 0.
I think constructing such a deterministic system, in which a division by 0 was defineable and had a deterministic result would be an advantage though. The question would be over the tradeoffs that would need to be made elsewhere in order to allow for this and it may not be useful enough to be applied in general (though I think by maintaining a record of which dimension the zero was constructed, the indeterminism of having all zeroes equal to each other could be removed and we would be able to linearly correlate between zeroes in multiple dimensions).
For example, if we multiply a inch by 2 we have 2 inches, but if we multiply an inch by zero we shouldn't get an unadulterated 0 but instead 0 inches. So a multiplication of a variable x by 0 should create 0x and not 0. Normal this isn't an issue when the constant coefficient is non-zero because x can vary and the resulting variation in the scaling is not ignorable and a linear relationship to x is specified, but when we define a multiplication by 0 to construct a non-descript 0 then for multiplication, this isn't sufficiently deterministics as it destroys linear information and hence we can't later compute an inverse and divide by 0, but if the information was retained, then we could invert a multiplication by zero and reconstruct the input (which happens to be necessary for many proofs, even if the end results are the same, they aren't provable correct and can degrade unless the influence of every input to every output is determinable).
As a matter of fact, I should post a thread on some ideas regarding this.
The act of division is the creation of groups using a defined quantity per group, this will naturally limit the quantity to being anything other than nothing. Or if you will look at it this way, a bunch of oranges are being divided into groups by zero, since zero is not a quantity, you can infinitely perfrom the divide operation and never get a result, therefore being undefined, unless you interrupt the operation which leaves you with 0 or infinite groups with the quantity of zero and a pile of oranges. No matter what is in the numerator, this will be the result every time.
If there ever is a solution to this, it will have to be an assumtion like "no good runner ever finishes a 100m race".
If there ever is a solution to this, it will have to be an assumtion like "no good runner ever finishes a 100m race".
Actually I created a thread here http://forum.physorg.com/index.php?act=ST&...t=0#entry301886 to allow for more deterministic notations constructing various infinite and infinitesimal quantities to be easier represented.
If we define 0=lim(1/n) as n->infinity and infinity=1/0, then we have a very precise manner in which to manipulate infinitesimal and infinite quantities and suddenly:
0/0=lim((1/n)/(1/n))=lim(n/n)=lim(1) as n->infinity
0/-0=-1
infinity*0^2=0
infinity*0=1
(1+0)^infinity=e~=2.7182818
0^0~=1-log(infinity)/infinity=1-0*log(infinity)
etc.
If we define 0=lim(1/n) as n->infinity and infinity=1/0, then we have a very precise manner in which to manipulate infinitesimal and infinite quantities and suddenly:
0/0=lim((1/n)/(1/n))=lim(n/n)=lim(1) as n->infinity
0/-0=-1
infinity*0^2=0
infinity*0=1
(1+0)^infinity=e~=2.7182818
0^0~=1-log(infinity)/infinity=1-0*log(infinity)
etc.
How can you define infinity as 1/0? That would be infinite operations, not an infinite quantity.
QUOTE (nabiul+Jan 14 2008, 06:58 AM)
How can you define infinity as 1/0? That would be infinite operations, not an infinite quantity.
I posted a link here http://forum.physorg.com/index.php?showtop...ndpost&p=301886 where I showed how a notation defining:
infinity=lim(n) as n->infinity
0=lim(1/n) as n->infinity
Can then be utilize to construct many other identities that are normally intuitive but not defined in a sufficiently precise manner to mathematical prove them as being identities:
For example we would expect that 1/infinity should be a value close to 0 and it is because:
1/infinity=lim(1/n) as n->infinity
And the limit of 1/1,1/2,1/3,1/4,1/5,... is bounded by 0, so we could write:
1/infinity=0
As well as:
0*infinity=1=lim(n*(1/n))=lim(n/n)=lim(1) as n->infinity
Or we could express Euler's Constant, the base of the natural log in this form as:
2.718281828~=e=(1+0)^infinity=lim((1+1/n)^n) as n->infinity
And then we could determine that:
0^0~=1+log(infinity)/infinity
etc.
We could also use these to describe geometric conversions between different dimensional forms.
For example an "infinite" number of points constructs a line, though in the case we'd have a precise mathematical definition of that infinite value and could construct a surface instead using an infinity^2 term or 2 surfaces as 2*infinity^2 etc.
We could create a fractal line in various was as, for example, log(infinity)*infinity and various other manipulations of 0 and infinite scalings.
Though notice that there would be no precise 0 in this case and that 0^2 would not be identical to 0, though we could still truncate infinitesimal values when we wanted a finite approximation and in this case we'd remove the 0s and infinite terms by computing the limit.
I posted a link here http://forum.physorg.com/index.php?showtop...ndpost&p=301886 where I showed how a notation defining:
infinity=lim(n) as n->infinity
0=lim(1/n) as n->infinity
Can then be utilize to construct many other identities that are normally intuitive but not defined in a sufficiently precise manner to mathematical prove them as being identities:
For example we would expect that 1/infinity should be a value close to 0 and it is because:
1/infinity=lim(1/n) as n->infinity
And the limit of 1/1,1/2,1/3,1/4,1/5,... is bounded by 0, so we could write:
1/infinity=0
As well as:
0*infinity=1=lim(n*(1/n))=lim(n/n)=lim(1) as n->infinity
Or we could express Euler's Constant, the base of the natural log in this form as:
2.718281828~=e=(1+0)^infinity=lim((1+1/n)^n) as n->infinity
And then we could determine that:
0^0~=1+log(infinity)/infinity
etc.
We could also use these to describe geometric conversions between different dimensional forms.
For example an "infinite" number of points constructs a line, though in the case we'd have a precise mathematical definition of that infinite value and could construct a surface instead using an infinity^2 term or 2 surfaces as 2*infinity^2 etc.
We could create a fractal line in various was as, for example, log(infinity)*infinity and various other manipulations of 0 and infinite scalings.
Though notice that there would be no precise 0 in this case and that 0^2 would not be identical to 0, though we could still truncate infinitesimal values when we wanted a finite approximation and in this case we'd remove the 0s and infinite terms by computing the limit.
I would advise to read Euler Differential Calculus and Books on Non-standard analysis (Abraham Robinson, Robert Goldblatt) .
"Infinitisemal Calculus" by Heinle, Kleinberg is especially good, as it runs both infinitesimal and limit based versions in paralel.
Infinitisemal Calculus by Heinle, Kleinberg in Amazon.com
They give simple, intuitive and rigorous defintions on how to handle infinitesimals in one scale.
By the way, infinitesimal/infinitesimal IS NOT 1- it is any finite quantity if infinitesimals are of the same order of magnitude, 0, if infinitesimal^2/infinitesimal.
Infinity is just 1/ infinitesimal, or infinitesimal /infinitesimal^2 etc.
It is very simple up to this point.
From here, since infinity = 1/infinitesimal,
infinity/infinity = any finite value
infinity^2/infinity=infinity
infinity/infinity^2 = 0
etc.
I do not quite understand Steven why should we develop new notations for so simple things?
A notation for infinitesimal in one scale is dx, dy etc......
If we want to go outside 1 scale, than there is almost nothing today ( May be prof Bells Smooth infinitesimal analysis in that direction as it involves imaginary infinitesimal iepsilon as replacing ict in theory of relativity-which is a step in the right direction):
Prof. Bell Preprints
Read e.g. "An Invitation to Smooth Infinitesimal Analysis"
"Infinitisemal Calculus" by Heinle, Kleinberg is especially good, as it runs both infinitesimal and limit based versions in paralel.
Infinitisemal Calculus by Heinle, Kleinberg in Amazon.com
They give simple, intuitive and rigorous defintions on how to handle infinitesimals in one scale.
By the way, infinitesimal/infinitesimal IS NOT 1- it is any finite quantity if infinitesimals are of the same order of magnitude, 0, if infinitesimal^2/infinitesimal.
Infinity is just 1/ infinitesimal, or infinitesimal /infinitesimal^2 etc.
It is very simple up to this point.
From here, since infinity = 1/infinitesimal,
infinity/infinity = any finite value
infinity^2/infinity=infinity
infinity/infinity^2 = 0
etc.
I do not quite understand Steven why should we develop new notations for so simple things?
A notation for infinitesimal in one scale is dx, dy etc......
If we want to go outside 1 scale, than there is almost nothing today ( May be prof Bells Smooth infinitesimal analysis in that direction as it involves imaginary infinitesimal iepsilon as replacing ict in theory of relativity-which is a step in the right direction):
Prof. Bell Preprints
Read e.g. "An Invitation to Smooth Infinitesimal Analysis"
QUOTE (Ivars+Jan 14 2008, 08:04 AM)
I would advise to read Euler Differential Calculus and Books on Non-standard analysis (Abraham Robinson, Robert Goldblatt) .
"Infinitisemal Calculus" by Heinle, Kleinberg is especially good, as it runs both infinitesimal and limit based versions in paralel.
Infinitisemal Calculus by Heinle, Kleinberg in Amazon.com
They give simple, intuitive and rigorous defintions on how to handle infinitesimals in one scale.
By the way, infinitesimal/infinitesimal IS NOT 1- it is any finite quantity if infinitesimals are of the same order of magnitude, 0, if infinitesimal^2/infinitesimal.
Infinity is just 1/ infinitesimal, or infinitesimal /infinitesimal^2 etc.
It is very simple up to this point.
From here, since infinity = 1/infinitesimal,
infinity/infinity = any finite value
infinity^2/infinity=infinity
infinity/infinity^2 = 0
etc.
I do not quite understand Steven why should we develop new notations for so simple things?
A notation for infinitesimal in one scale is dx, dy etc......
If we want to go outside 1 scale, than there is almost nothing today ( May be prof Bells Smooth infinitesimal analysis in that direction as it involves imaginary infinitesimal iepsilon as replacing ict in theory of relativity-which is a step in the right direction):
Prof. Bell Preprints
Read e.g. "An Invitation to Smooth Infinitesimal Analysis"
(BTW, thank you for the great link at the bottom of your post. There's a lot of great information there
)
Yes, normally we'd expect infinitesimal and infinite quantities to be undefined and at a minimum allow for some finite error, but if you check out the link I posted, I constructed a precise definition for 0 and infinity in order to avoid this.
So my above post was made with regard to the notation used in this thread http://forum.physorg.com/index.php?showtop...=0&#entry301886, in which case there aren't even finite differences (except to the point an approximation for infinitesimal terms is used, and then we would have errors if we attempted to use an alternate infinitesimal reference for measurement).
Yes, if most everyone had a good understand of computing limits then it would be a non-issue, but that are many realms that are influenced by a similar problem and it ultimately appears to stem from assuming that all 0s are identically nothing, just as all infinities are assumed to be identical.
Hej Steven
Obviously they are different. Just forget the limits and 1 dimensional real number line when You think about these things. I know You do, did not want to sound like I sounded. Also Integers have no place in infinite limits as simplest infinity is beyond them.
Regarding an average you bring up a new context in which a 0 can be used (and I admit I avoided it in my prior posts intentionally because it brings yet another version of 0 that's often used).
In the case of defining 0 to be a limit of 1/n as n->infinity, we're considering 0 in terms of a scaling that shrinks or reduces the range over which numbers span in size, but there's another context used in mathematics for 0 and that's in terms of a shift or offset by nothing - in other words instead of shrinking a dimension to a point, we're adding nothing to a quantity and remaining in the same state afterwards.
From a geometric perspective, if the width of a point is 0 relative to the length of a line, then we're using this in the perspective of a scaling that implies it takes an "infinite" number of points to make a line. In that case if we added up an infinite number of these "0" widths, we should come up with something that spans a line, but if we're instead using a 0 that's constructed to represent the sum of two opposing and equal forces that cancel, then an infinite summation of these wouldn't diverge from remaining cancelled in their influence.
In the linear context an average value might be a useful definition, but for the scaling context the geometric mean of two quantities m=sqrt(a*
tends to be better in that we can swap a*b with m*m, or a*b=m*m and so m can be seen as a "multiplicative average" of a and b, in a sense quite similar to a linear average avg=(a+/2 creates a quantity for which a+b=avg+avg.
So you brought up yet another issue regarding zero that's often overlooked as well.
And in your turn, you too have hit the nail on the head. That's the 'BALANCED' or 'TRANSITION ZONE' 'common/superposition point' between converging ranges/forces I have been speaking of in my 'contextual mathematics' observations re the "0" concept, hehehe.
Things seem to be converging for our various approaches/discussions, steven, Ivars, Raphie et al!
This is good; and as it should be for 'explorers in the same 'landscape', hehehe.
Cheers and goodnight, all!
RC.
.
.0.............(Bar)1 ^.0.........(BAR)1 EQUALS 1 Right!
Negative over Negative, Positive over Positive, Negative over Positive, Positive over Negative.
Though "you can't get there from here" it seems to approach 1.......
"Infinitisemal Calculus" by Heinle, Kleinberg is especially good, as it runs both infinitesimal and limit based versions in paralel.
Infinitisemal Calculus by Heinle, Kleinberg in Amazon.com
They give simple, intuitive and rigorous defintions on how to handle infinitesimals in one scale.
By the way, infinitesimal/infinitesimal IS NOT 1- it is any finite quantity if infinitesimals are of the same order of magnitude, 0, if infinitesimal^2/infinitesimal.
Infinity is just 1/ infinitesimal, or infinitesimal /infinitesimal^2 etc.
It is very simple up to this point.
From here, since infinity = 1/infinitesimal,
infinity/infinity = any finite value
infinity^2/infinity=infinity
infinity/infinity^2 = 0
etc.
I do not quite understand Steven why should we develop new notations for so simple things?
A notation for infinitesimal in one scale is dx, dy etc......
If we want to go outside 1 scale, than there is almost nothing today ( May be prof Bells Smooth infinitesimal analysis in that direction as it involves imaginary infinitesimal iepsilon as replacing ict in theory of relativity-which is a step in the right direction):
Prof. Bell Preprints
Read e.g. "An Invitation to Smooth Infinitesimal Analysis"
(BTW, thank you for the great link at the bottom of your post. There's a lot of great information there
)Yes, normally we'd expect infinitesimal and infinite quantities to be undefined and at a minimum allow for some finite error, but if you check out the link I posted, I constructed a precise definition for 0 and infinity in order to avoid this.
So my above post was made with regard to the notation used in this thread http://forum.physorg.com/index.php?showtop...=0&#entry301886, in which case there aren't even finite differences (except to the point an approximation for infinitesimal terms is used, and then we would have errors if we attempted to use an alternate infinitesimal reference for measurement).
QUOTE (Ivars+)
I do not quite understand Steven why should we develop new notations for so simple things?
Because many people appear to have problems recognizing that multiplication by 0 isn't a linear operation and also appear to assume that .999... must equal 1 etc.
The issue is primarily with regard to computing limits.
Yes, if most everyone had a good understand of computing limits then it would be a non-issue, but that are many realms that are influenced by a similar problem and it ultimately appears to stem from assuming that all 0s are identically nothing, just as all infinities are assumed to be identical.
There's also the issue of the non-standard '...' recursive operation used. A specific and deterministic definition needs to be constructed for an operation such as computing an infinite summation 1/2+1/4+1/8+...
In this case the '...' should have a precise mathematical notation and in this case, this summation should be seen as:
lim((2^n-1)/(2^n)) as n->infinity
And not as 1/2+1/4+1/8+...=1 as the 1 is the limit of the summation and not the infinite sum.
With a precise definition for such symbols we'd have many fewer pages of debates over these issues because people couldn't switch contexts as to what 0 or infinity means in one case or another.
Though an additional problem is that many people don't understand that results are only reliable for infinitesimal operations when a limit is computed once for a result and not applied at multiple stages of a computation.
For example, with the above notation, 1+0 represents (1+1/n) as n->infinity, which can become very close to 1 but 1+0 can't always be rewritten as 1 if we're going to perform further computations with this value, such as (1+0)^infinity=e~=2.71828, where 1^infinity=1, yet some people may mistakenly say that 1+0=1 and then assume that this 1 is a precise result and not simply a limit to the 1+1/n term.
Overall, I've seen a lot of misperceptions from people who should be quite well educated (at least that's what many of them claim) and should understand these differences, but it's likely a more concise and deterministic manner in which to handle infinite and infinitesimal quantities would help to clarify how these operations work.
Because many people appear to have problems recognizing that multiplication by 0 isn't a linear operation and also appear to assume that .999... must equal 1 etc.
The issue is primarily with regard to computing limits.
Yes, if most everyone had a good understand of computing limits then it would be a non-issue, but that are many realms that are influenced by a similar problem and it ultimately appears to stem from assuming that all 0s are identically nothing, just as all infinities are assumed to be identical.
There's also the issue of the non-standard '...' recursive operation used. A specific and deterministic definition needs to be constructed for an operation such as computing an infinite summation 1/2+1/4+1/8+...
In this case the '...' should have a precise mathematical notation and in this case, this summation should be seen as:
lim((2^n-1)/(2^n)) as n->infinity
And not as 1/2+1/4+1/8+...=1 as the 1 is the limit of the summation and not the infinite sum.
With a precise definition for such symbols we'd have many fewer pages of debates over these issues because people couldn't switch contexts as to what 0 or infinity means in one case or another.
Though an additional problem is that many people don't understand that results are only reliable for infinitesimal operations when a limit is computed once for a result and not applied at multiple stages of a computation.
For example, with the above notation, 1+0 represents (1+1/n) as n->infinity, which can become very close to 1 but 1+0 can't always be rewritten as 1 if we're going to perform further computations with this value, such as (1+0)^infinity=e~=2.71828, where 1^infinity=1, yet some people may mistakenly say that 1+0=1 and then assume that this 1 is a precise result and not simply a limit to the 1+1/n term.
Overall, I've seen a lot of misperceptions from people who should be quite well educated (at least that's what many of them claim) and should understand these differences, but it's likely a more concise and deterministic manner in which to handle infinite and infinitesimal quantities would help to clarify how these operations work.
QUOTE (StevenA+Jan 14 2008, 09:31 AM)
A specific and deterministic definition needs to be constructed for an operation such as computing an infinite summation 1/2+1/4+1/8+...
In this case the '...' should have a precise mathematical notation and in this case, this summation should be seen as:
lim((2^n-1)/(2^n)) as n->infinity
And not as 1/2+1/4+1/8+...=1 as the 1 is the limit of the summation and not the infinite sum.
Learn what a Taylor expansion is.
http://www.dpmms.cam.ac.uk/~twk/C5.pdf
Learn that. I bet you can't do the example sheets at the end.
In this case the '...' should have a precise mathematical notation and in this case, this summation should be seen as:
lim((2^n-1)/(2^n)) as n->infinity
And not as 1/2+1/4+1/8+...=1 as the 1 is the limit of the summation and not the infinite sum.
Learn what a Taylor expansion is.
http://www.dpmms.cam.ac.uk/~twk/C5.pdf
Learn that. I bet you can't do the example sheets at the end.
QUOTE (StevenA+Jan 14 2008, 08:31 AM)
Yes, if most everyone had a good understand of computing limits then it would be a non-issue, but that are many realms that are influenced by a similar problem and it ultimately appears to stem from assuming that all 0s are identically nothing, just as all infinities are assumed to be identical.
Hej Steven
Obviously they are different. Just forget the limits and 1 dimensional real number line when You think about these things. I know You do, did not want to sound like I sounded. Also Integers have no place in infinite limits as simplest infinity is beyond them.
.
Hi guys!
Just out of curiosity, and I've always wondered about this....
When one uses the expression:
......as n->infinity
WHICH PARTICULAR 'infinity' is being 'approached' by the number 'n' if 'infinity' ISN'T a NUMBER?
Thanks.
Back tomorrow. Good night!
RC.
.
Hi guys!
Just out of curiosity, and I've always wondered about this....
When one uses the expression:
......as n->infinity
WHICH PARTICULAR 'infinity' is being 'approached' by the number 'n' if 'infinity' ISN'T a NUMBER?
Thanks.
Back tomorrow. Good night!
RC.
.
QUOTE (Ivars+Jan 14 2008, 08:04 AM)
I do not quite understand Steven why should we develop new notations for so simple things?
Dear Ivars,
In response:
In order to have new ways of looking at the complex "things," which arise from the simple ones.
Best,
Raphie
==============================================================
P.S. For me, my NON-STANDARD (i.e. Kolo Math ©) convention is to treat 0/0 as BOTH 0 and infinity, with an average value of infinity/2. Why?
Every fraction is composed of TWO, not one, term(s), call them A and B...
Let...
A = 0/x = 0
B = x/0 = undefined (Standard Math Definition)
B' = x/0 = infinity (Kolo Math Convention)
where x = 0
Then...
A = 0/0
B' = 0/0
... meaning we can add the two terms together since they share the same denominator...
A + B' = C
and divide by 2 to get, not the value, but the AVERAGE value.
Let...
infinity (the concept) == z (the largest number imaginable)
(A + B')/2 == (0 + z)/2 = z/2
z/2 == 0/0 == infinity/2
Dear Ivars,
In response:
In order to have new ways of looking at the complex "things," which arise from the simple ones.
Best,
Raphie
==============================================================
P.S. For me, my NON-STANDARD (i.e. Kolo Math ©) convention is to treat 0/0 as BOTH 0 and infinity, with an average value of infinity/2. Why?
Every fraction is composed of TWO, not one, term(s), call them A and B...
Let...
A = 0/x = 0
B = x/0 = undefined (Standard Math Definition)
B' = x/0 = infinity (Kolo Math Convention)
where x = 0
Then...
A = 0/0
B' = 0/0
... meaning we can add the two terms together since they share the same denominator...
A + B' = C
and divide by 2 to get, not the value, but the AVERAGE value.
Let...
infinity (the concept) == z (the largest number imaginable)
(A + B')/2 == (0 + z)/2 = z/2
z/2 == 0/0 == infinity/2
QUOTE (RealityCheck+Jan 14 2008, 08:58 AM)
.
Hi guys!
Just out of curiosity, and I've always wondered about this....
When one uses the expression:
......as n->infinity
WHICH PARTICULAR 'infinity' is being 'approached' by the number 'n' if 'infinity' ISN'T a NUMBER?
Thanks.
Back tomorrow. Good night!
RC.
.
Yes, you hit the nail on the head, RealityCheck.
For a limit to be a valid computation, only one limit to a sequence should be computed, otherwise there is no single infinite term in the equation and each limit computation now becomes a finite value relative to other limit computations, which violates them each being considered infinite relative to each other.
So a good example of the problem would be to compute:
x=lim(m) as m->infinity
y=lim(x/n) as n->infinity
In this case the typical response is that x is undefined, because there isn't a specific limit to m and in this case the limit of x/n would also become indeterminant, but truly we could recognize that a function could be constructed that would compute the ratio of m/n and it could be any value between 0 and some vague infinite value.
Whereas the same construction can be performed in a (more, though likely still not entirely for all purposes) determinant way as:
x=f(n)
y=lim(x/n) as n->infinity
Then we can actually define a multiplication by 0 to be a division by n or multiplication by 1/n etc. and only one "infinite" term is present, in order to remove the indeterminacies of which "infinite" quantity is being referred to.
(Though I'd still have to add that in many ways a precise terminology regarding these computations would be to refer to "approaching infinity" or being "unbounded" instead of "being infinite", which tends to convey a precision that typically doesn't exist)
Hi guys!
Just out of curiosity, and I've always wondered about this....
When one uses the expression:
......as n->infinity
WHICH PARTICULAR 'infinity' is being 'approached' by the number 'n' if 'infinity' ISN'T a NUMBER?
Thanks.
Back tomorrow. Good night!
RC.
.
Yes, you hit the nail on the head, RealityCheck.
For a limit to be a valid computation, only one limit to a sequence should be computed, otherwise there is no single infinite term in the equation and each limit computation now becomes a finite value relative to other limit computations, which violates them each being considered infinite relative to each other.
So a good example of the problem would be to compute:
x=lim(m) as m->infinity
y=lim(x/n) as n->infinity
In this case the typical response is that x is undefined, because there isn't a specific limit to m and in this case the limit of x/n would also become indeterminant, but truly we could recognize that a function could be constructed that would compute the ratio of m/n and it could be any value between 0 and some vague infinite value.
Whereas the same construction can be performed in a (more, though likely still not entirely for all purposes) determinant way as:
x=f(n)
y=lim(x/n) as n->infinity
Then we can actually define a multiplication by 0 to be a division by n or multiplication by 1/n etc. and only one "infinite" term is present, in order to remove the indeterminacies of which "infinite" quantity is being referred to.
(Though I'd still have to add that in many ways a precise terminology regarding these computations would be to refer to "approaching infinity" or being "unbounded" instead of "being infinite", which tends to convey a precision that typically doesn't exist)
QUOTE (Raphie Frank+Jan 14 2008, 09:15 AM)
Dear Ivars,
In response:
In order to have new ways of looking at the complex "things," which arise from the simple ones.
Best,
Raphie
==============================================================
P.S. For me, my NON-STANDARD (i.e. Kolo Math ©) convention is to treat 0/0 as BOTH 0 and infinity, with an average value of infinity/2. Why?
Every fraction is composed of TWO, not one, term(s), call them A and B...
Let...
A = 0/x = 0
B = x/0 = undefined (Standard Math Definition)
B' = x/0 = infinity (Kolo Math Convention)
where x = 0
Then...
A = 0/0
B' = 0/0
... meaning we can add the two terms together since they share the same denominator...
A + B' = C
and divide by 2 to get, not the value, but the AVERAGE value.
Let...
infinity (the concept) == z (the largest number imaginable)
(A + B')/2 == (0 + z)/2 = z/2
0/0 == z/2 == infinity/2
Regarding an average you bring up a new context in which a 0 can be used (and I admit I avoided it in my prior posts intentionally because it brings yet another version of 0 that's often used).
In the case of defining 0 to be a limit of 1/n as n->infinity, we're considering 0 in terms of a scaling that shrinks or reduces the range over which numbers span in size, but there's another context used in mathematics for 0 and that's in terms of a shift or offset by nothing - in other words instead of shrinking a dimension to a point, we're adding nothing to a quantity and remaining in the same state afterwards.
From a geometric perspective, if the width of a point is 0 relative to the length of a line, then we're using this in the perspective of a scaling that implies it takes an "infinite" number of points to make a line. In that case if we added up an infinite number of these "0" widths, we should come up with something that spans a line, but if we're instead using a 0 that's constructed to represent the sum of two opposing and equal forces that cancel, then an infinite summation of these wouldn't diverge from remaining cancelled in their influence.
In the linear context an average value might be a useful definition, but for the scaling context the geometric mean of two quantities m=sqrt(a*b) tends to be better in that we can swap a*b with m*m, or a*b=m*m and so m can be seen as a "multiplicative average" of a and b, in a sense quite similar to a linear average avg=(a+b)/2 creates a quantity for which a+b=avg+avg.
So you brought up yet another issue regarding zero that's often overlooked as well.
In response:
In order to have new ways of looking at the complex "things," which arise from the simple ones.
Best,
Raphie
==============================================================
P.S. For me, my NON-STANDARD (i.e. Kolo Math ©) convention is to treat 0/0 as BOTH 0 and infinity, with an average value of infinity/2. Why?
Every fraction is composed of TWO, not one, term(s), call them A and B...
Let...
A = 0/x = 0
B = x/0 = undefined (Standard Math Definition)
B' = x/0 = infinity (Kolo Math Convention)
where x = 0
Then...
A = 0/0
B' = 0/0
... meaning we can add the two terms together since they share the same denominator...
A + B' = C
and divide by 2 to get, not the value, but the AVERAGE value.
Let...
infinity (the concept) == z (the largest number imaginable)
(A + B')/2 == (0 + z)/2 = z/2
0/0 == z/2 == infinity/2
Regarding an average you bring up a new context in which a 0 can be used (and I admit I avoided it in my prior posts intentionally because it brings yet another version of 0 that's often used).
In the case of defining 0 to be a limit of 1/n as n->infinity, we're considering 0 in terms of a scaling that shrinks or reduces the range over which numbers span in size, but there's another context used in mathematics for 0 and that's in terms of a shift or offset by nothing - in other words instead of shrinking a dimension to a point, we're adding nothing to a quantity and remaining in the same state afterwards.
From a geometric perspective, if the width of a point is 0 relative to the length of a line, then we're using this in the perspective of a scaling that implies it takes an "infinite" number of points to make a line. In that case if we added up an infinite number of these "0" widths, we should come up with something that spans a line, but if we're instead using a 0 that's constructed to represent the sum of two opposing and equal forces that cancel, then an infinite summation of these wouldn't diverge from remaining cancelled in their influence.
In the linear context an average value might be a useful definition, but for the scaling context the geometric mean of two quantities m=sqrt(a*b) tends to be better in that we can swap a*b with m*m, or a*b=m*m and so m can be seen as a "multiplicative average" of a and b, in a sense quite similar to a linear average avg=(a+b)/2 creates a quantity for which a+b=avg+avg.
So you brought up yet another issue regarding zero that's often overlooked as well.
Dear StevenA,
It's all a question of "reference frames."
Speaking of which...
The Reference Frame
(the blog of Lubos Motl)
http://motls.blogspot.com/
Best,
Raphie
It's all a question of "reference frames."
Speaking of which...
The Reference Frame
(the blog of Lubos Motl)
http://motls.blogspot.com/
Best,
Raphie
QUOTE (StevenA+Jan 14 2008, 09:48 AM)
Regarding an average you bring up a new context in which a 0 can be used (and I admit I avoided it in my prior posts intentionally because it brings yet another version of 0 that's often used).
In the case of defining 0 to be a limit of 1/n as n->infinity, we're considering 0 in terms of a scaling that shrinks or reduces the range over which numbers span in size, but there's another context used in mathematics for 0 and that's in terms of a shift or offset by nothing - in other words instead of shrinking a dimension to a point, we're adding nothing to a quantity and remaining in the same state afterwards.
From a geometric perspective, if the width of a point is 0 relative to the length of a line, then we're using this in the perspective of a scaling that implies it takes an "infinite" number of points to make a line. In that case if we added up an infinite number of these "0" widths, we should come up with something that spans a line, but if we're instead using a 0 that's constructed to represent the sum of two opposing and equal forces that cancel, then an infinite summation of these wouldn't diverge from remaining cancelled in their influence.
In the linear context an average value might be a useful definition, but for the scaling context the geometric mean of two quantities m=sqrt(a*
tends to be better in that we can swap a*b with m*m, or a*b=m*m and so m can be seen as a "multiplicative average" of a and b, in a sense quite similar to a linear average avg=(a+/2 creates a quantity for which a+b=avg+avg.So you brought up yet another issue regarding zero that's often overlooked as well.
And in your turn, you too have hit the nail on the head. That's the 'BALANCED' or 'TRANSITION ZONE' 'common/superposition point' between converging ranges/forces I have been speaking of in my 'contextual mathematics' observations re the "0" concept, hehehe.
Things seem to be converging for our various approaches/discussions, steven, Ivars, Raphie et al!
This is good; and as it should be for 'explorers in the same 'landscape', hehehe.
Cheers and goodnight, all!
RC.
.
QUOTE (RealityCheck+Jan 14 2008, 04:58 AM)
When one uses the expression:
......as n->infinity
WHICH PARTICULAR 'infinity' is being 'approached' by the number 'n' if 'infinity' ISN'T a NUMBER?
The question only gives validity to an answer (any answer whatsoever) if you invent a REAL, physical "momentum" for the operation of "approaching infinity".
......as n->infinity
WHICH PARTICULAR 'infinity' is being 'approached' by the number 'n' if 'infinity' ISN'T a NUMBER?
The question only gives validity to an answer (any answer whatsoever) if you invent a REAL, physical "momentum" for the operation of "approaching infinity".
QUOTE (IAMoraes+Jan 14 2008, 10:19 AM)
The question only gives validity to an answer (any answer whatsoever) if you invent a REAL, physical "momentum" for the operation of "approaching infinity".
Hi IAMoraes!
I know what you are getting at, mate.
BUT the 'infinity' not being ANY sort of NUMBER even in the 'static maths' conventions used for the static number line concept and its 'limits' conventions, then it doesn't matter whether one is using it conventionally or unconventionally in such an expression as "....n->infinity".
It STILL ASSUMES some 'definite' infinity OR it is ALL AT SEA as to WHICH 'infinity' it is 'talking about', hehehe.
Either way....the question stands.
See what I mean?
Oh, and you're right...the answer HAS to be REAL for any 'discrimination/meaning' to attach to the 'answer'...whatever that will turn out to be.
Well SPOTTED, mate!
G-night mate!
RC.
.
Hi IAMoraes!
I know what you are getting at, mate.
BUT the 'infinity' not being ANY sort of NUMBER even in the 'static maths' conventions used for the static number line concept and its 'limits' conventions, then it doesn't matter whether one is using it conventionally or unconventionally in such an expression as "....n->infinity".
It STILL ASSUMES some 'definite' infinity OR it is ALL AT SEA as to WHICH 'infinity' it is 'talking about', hehehe.
Either way....the question stands.
See what I mean?
Oh, and you're right...the answer HAS to be REAL for any 'discrimination/meaning' to attach to the 'answer'...whatever that will turn out to be.
Well SPOTTED, mate!
G-night mate!
RC.
.
I was thinking once why 0/x=0 and x/0 is incorect? And made conclusion that just need somehow in math to describe imposible things or so. It's would be ok if x/0=0 and 0/x=incorect, but just from traditions things going on how they are now.
QUOTE (IAMoraes+Jan 14 2008, 10:19 AM)
The question only gives validity to an answer (any answer whatsoever) if you invent a REAL, physical "momentum" for the operation of "approaching infinity".
And I believe this REAL infinity should be seen as time. Time is the real potentially infinite source for quantity. Everything we work with in a moment is finite, but given enough time ... who knows.
Also, most all infinite concepts are constructed not as specific static states or quantities but instead as processes with potential.
There was an example on another thread of putting people into an infinitely large hotel. Of course the example never actually tried to describe how large an infinitely size hotel is relative to other possible infinite things, but instead simply described a process, that given a potentially infinite amount of time and people could be continually restructed to accomodate everyone.
So in this case infinity would be a function of time and not a specific number.
And I believe this REAL infinity should be seen as time. Time is the real potentially infinite source for quantity. Everything we work with in a moment is finite, but given enough time ... who knows.
Also, most all infinite concepts are constructed not as specific static states or quantities but instead as processes with potential.
There was an example on another thread of putting people into an infinitely large hotel. Of course the example never actually tried to describe how large an infinitely size hotel is relative to other possible infinite things, but instead simply described a process, that given a potentially infinite amount of time and people could be continually restructed to accomodate everyone.
So in this case infinity would be a function of time and not a specific number.
This is a reply to that infinity=1/0 thing last page.
Yes 0= 1/n as n-> infinity,but you cannot just switch the numbers out to get infinity=1/0. Thats pretty much breaking the rules of mathematics.
0=1/n, as n-> infinity (multiply by n)
n*0=(1/n)*n
n*0 makes,... 0, which leaves us with 0=1, care the explain mate how you turned 0=1/n into n=1/0 ?
Also even if you thought of the LS being n*0=1, which in real math you don't do, you would have to divide out the zero to bring it over to the RS, which you can't do.
Yes 0= 1/n as n-> infinity,but you cannot just switch the numbers out to get infinity=1/0. Thats pretty much breaking the rules of mathematics.
0=1/n, as n-> infinity (multiply by n)
n*0=(1/n)*n
n*0 makes,... 0, which leaves us with 0=1, care the explain mate how you turned 0=1/n into n=1/0 ?
Also even if you thought of the LS being n*0=1, which in real math you don't do, you would have to divide out the zero to bring it over to the RS, which you can't do.
.0.............(Bar)1 ^.0.........(BAR)1 EQUALS 1 Right!Negative over Negative, Positive over Positive, Negative over Positive, Positive over Negative.
Though "you can't get there from here" it seems to approach 1.......
Regarding the IRS equation above.
As much as I would like to accept the idea, your equation does not work that way. It is true that as long as you apply the same function to each side of the equals sign, the sides will remain the same in relation to each other. However, your equation only represents the relationship between how much you owe the IRS and how much you are going to pay. Your equation only states that you will pay the IRS zero dollars if you owe them zero dollars.
As much as I would like to accept the idea, your equation does not work that way. It is true that as long as you apply the same function to each side of the equals sign, the sides will remain the same in relation to each other. However, your equation only represents the relationship between how much you owe the IRS and how much you are going to pay. Your equation only states that you will pay the IRS zero dollars if you owe them zero dollars.
Sorry to reply twice consecutively, but I have another statement.
I must disagree with the statement in the title of the topic that infinity divided by infinity equals one. If we take any value, fraction or not, and convert it into fraction form if necessary, we can multiply both sides of the fraction by infinity, an action that is stated through some property (which I wish not to spent time looking up) as not changing the fraction value. Thus, we must assume that the end result, which happen to be infinity over infinity (unless you had a zero in the denominator or numerator) is equal to the previous fraction. Furthermore, infinity over infinity must be able to equal any value, because all values can be simplified (or rather un-simplified) to it.
I must disagree with the statement in the title of the topic that infinity divided by infinity equals one. If we take any value, fraction or not, and convert it into fraction form if necessary, we can multiply both sides of the fraction by infinity, an action that is stated through some property (which I wish not to spent time looking up) as not changing the fraction value. Thus, we must assume that the end result, which happen to be infinity over infinity (unless you had a zero in the denominator or numerator) is equal to the previous fraction. Furthermore, infinity over infinity must be able to equal any value, because all values can be simplified (or rather un-simplified) to it.
the answer in 0/0 is 1
because x/x=1
then x=0
hehe
because x/x=1
then x=0
hehe
How many times can you subtract 0 from 0? infinite
How many times can you subtract 1 from 1? 1
How many times can you subtract 1 from 0? 0
That's why 0/0 = infinite
Silly people.
How many times can you subtract 1 from 1? 1
How many times can you subtract 1 from 0? 0
That's why 0/0 = infinite
Silly people.
x/1 means you are dividing x into 1 piece.
x/0 means you are dividing x into zero pieces.
Does that make sense? No. Think about that in your head. You have some apples and i tell you to divide them into zero pieces. What does that even mean? Nothing. You can't do it. That's why the calculator says "cannot divide by zero". It's not complicated.
x/0 means you are dividing x into zero pieces.
Does that make sense? No. Think about that in your head. You have some apples and i tell you to divide them into zero pieces. What does that even mean? Nothing. You can't do it. That's why the calculator says "cannot divide by zero". It's not complicated.
QUOTE (Latrosicarius+Aug 5 2009, 08:02 PM)
x/1 means you are dividing x into 1 piece.
x/0 means you are dividing x into zero pieces.
Does that make sense? No. Think about that in your head. You have some apples and i tell you to divide them into zero pieces. What does that even mean? Nothing. You can't do it. That's why the calculator says "cannot divide by zero". It's not complicated.
Using this example, I would say that the answer would be equal to the size of the apple pieces. If you cut them into 0 pieces, you would have infinite apples.
x/0 means you are dividing x into zero pieces.
Does that make sense? No. Think about that in your head. You have some apples and i tell you to divide them into zero pieces. What does that even mean? Nothing. You can't do it. That's why the calculator says "cannot divide by zero". It's not complicated.
Using this example, I would say that the answer would be equal to the size of the apple pieces. If you cut them into 0 pieces, you would have infinite apples.
You can't take something and split it into zero parts.
You can split it into one whole part. But not zero parts.
It's just not possible in real life.
If you look at division as repeated subtraction, then, yes, you will have to subtract zero infinite times and you will never get an answer because you never finish.
You can split it into one whole part. But not zero parts.
It's just not possible in real life.
If you look at division as repeated subtraction, then, yes, you will have to subtract zero infinite times and you will never get an answer because you never finish.
Those of you who are still not able to define what 0 is (null-zip-nothing), re-evalute your thoughs about nothing. Start with nothing (0) and make understandable, sensibe mathematics. If the result is 0/0=one, then you should do anything but physics!
QUOTE (Latrosicarius+Aug 5 2009, 08:16 PM)
You can't take something and split it into zero parts.
You can split it into one whole part. But not zero parts.
It's just not possible in real life.
If you look at division as repeated subtraction, then, yes, you will have to subtract zero infinite times and you will never get an answer because you never finish.
BUT, you can take 0 away from something infinite times. If you use subtraction instead of division, you get a clearer answer. How many times can I take 0 marbles out of a bag that has 0 marbles in it?
You can split it into one whole part. But not zero parts.
It's just not possible in real life.
If you look at division as repeated subtraction, then, yes, you will have to subtract zero infinite times and you will never get an answer because you never finish.
BUT, you can take 0 away from something infinite times. If you use subtraction instead of division, you get a clearer answer. How many times can I take 0 marbles out of a bag that has 0 marbles in it?
Those of you who are still not able to define what 0 is (null-zip-nothing), re-evalute your thoughs about nothing. Start with nothing (0) and make understandable, sensibe mathematics. If the result is 0/0=one, then you should do anything but physics!
All I know is when I see math with inf's or 0's in it I instantly know its BS math that can't possibly mean anything. I don't like math for this reason... It takes simple concepts and makes them impossible to explain to just about anyone. We humans seem to think we understand infinity and nothingness... We couldn't be more wrong about that. While we become more sure of our math we will find our selfs going more and more in the wrong direction from the truth.
QUOTE (magpies+Aug 5 2009, 04:15 PM)
All I know is when I see math with inf's or 0's in it I instantly know its BS math that can't possibly mean anything. I don't like math for this reason... It takes simple concepts and makes them impossible to explain to just about anyone. We humans seem to think we understand infinity and nothingness... We couldn't be more wrong about that. While we become more sure of our math we will find our selfs going more and more in the wrong direction from the truth.
So, you're not only an enemy of science, but you're an enemy of math too? Pardon me asking, but what is your highest completed education level?
So, you're not only an enemy of science, but you're an enemy of math too? Pardon me asking, but what is your highest completed education level?
High school... I went to college for accounting, electrial, auto repair... Couldn't stand any of thouse so I droped out each time... But honestly surfing the internet for like 15 years is my highest completed education besides knowing every thing inherently from birth if that counts...
Also im not an enemy of thouse things... I just know of better ways to think about the world. If someone told you living without food water or air was possible youd probably say they are crazy... before asking them how.
Also im not an enemy of thouse things... I just know of better ways to think about the world. If someone told you living without food water or air was possible youd probably say they are crazy... before asking them how.
QUOTE (magpies+Aug 5 2009, 04:26 PM)
High school... I went to college for accounting, electrial, auto repair... Couldn't stand any of thouse so I droped out each time... But honestly surfing the internet for like 15 years is my highest completed education besides knowing every thing inherently from birth if that counts...
This explains everything. You "couldn't stand" real education, so you resorted to "educating" yourself. Fail.
And yes, this means that you have contempt for science, math, and everything based on logic.
This explains everything. You "couldn't stand" real education, so you resorted to "educating" yourself. Fail.
And yes, this means that you have contempt for science, math, and everything based on logic.
Yeah because clearly I need someone to teach me how to tie my own shoes 
And I guess you are right I do have contempt for thouse things... but then again I have contempt for pretty much every thing if I think about it.
How did you learn to tie your shoes?
And I guess you are right I do have contempt for thouse things... but then again I have contempt for pretty much every thing if I think about it.
How did you learn to tie your shoes?
QUOTE (magpies+Aug 5 2009, 04:46 PM)
Yeah because clearly I need someone to teach me how to tie my own shoes
And I guess you are right I do have contempt for thouse things... but then again I have contempt for pretty much every thing if I think about it.
How did you learn to tie your shoes?
It sure-as-hell didn't take me 15 years to look up on the internet.
The real question is: Do you have contempt for knowledge because you were rejected? Or, were you rejected because of your contempt?
And I guess you are right I do have contempt for thouse things... but then again I have contempt for pretty much every thing if I think about it.
How did you learn to tie your shoes?
It sure-as-hell didn't take me 15 years to look up on the internet.
The real question is: Do you have contempt for knowledge because you were rejected? Or, were you rejected because of your contempt?
So thats the real question! Iv been looking for the real question for years amazing that you had it all this time.
Q: Do I have contempt for knowledge because I was rejected?
A: Probably as do you.
Q: Was I rejected because of my contempt?
A: Probably as were you.
Q: Do I have contempt for knowledge because I was rejected?
A: Probably as do you.
Q: Was I rejected because of my contempt?
A: Probably as were you.
QUOTE (Tor+Aug 5 2009, 09:27 PM)
Those of you who are still not able to define what 0 is (null-zip-nothing), re-evalute your thoughs about nothing. Start with nothing (0) and make understandable, sensibe mathematics. If the result is 0/0=one, then you should do anything but physics!
It's the identity of the binary operation of addition. 1 is the identity to the binary operation of multiplication. The reals are constructed by requiring its a group under addition and a semigroup under multiplication, meaning there's no multiplicative inverse of the additive identity. 1/0 is not '1 divided by 0', it's the multiplicative inverse of the additive identity, so doesm't exist.
It's the identity of the binary operation of addition. 1 is the identity to the binary operation of multiplication. The reals are constructed by requiring its a group under addition and a semigroup under multiplication, meaning there's no multiplicative inverse of the additive identity. 1/0 is not '1 divided by 0', it's the multiplicative inverse of the additive identity, so doesm't exist.
QUOTE (magpies+Aug 5 2009, 10:15 PM)
All I know is when I see math with inf's or 0's in it I instantly know its BS math that can't possibly mean anything. I don't like math for this reason... It takes simple concepts and makes them impossible to explain to just about anyone. We humans seem to think we understand infinity and nothingness... We couldn't be more wrong about that. While we become more sure of our math we will find our selfs going more and more in the wrong direction from the truth.
Without a zero you can't have such things as rings, algebras, vector spaces, kernels of linear transforms, the entire basis of mathematical physics vanishes. So you're wrong. You believe it's impossible to say anything about infinitely large sets because you haven't tried to learn or are incapable of learning. Your shortcomings are not mine.
And you fail to realize if we didnt have math and physics we would have some thing in its place and a much better some thing at that. Also it is impossible to use an infinitely large number in math without making the problem give the answer you want it to give. So... Your wrong. If your not wrong then please show me what infinity looks like by drawing a picture of it. A picture where I dont have to use my mind to make it work. K?
QUOTE (magpies+Aug 5 2009, 11:13 PM)
And you fail to realize if we didnt have math and physics we would have some thing in its place and a much better some thing at that.
If humanity was knocked back into the stone age and had to develop civilisation again we'd have new languages, new cultures, new art, new peoples, new everything except maths and science. They are univeral constants, they are things which transend cultures, languages and geography because they are somehow external to us.
If humanity was knocked back into the stone age and had to develop civilisation again we'd have new languages, new cultures, new art, new peoples, new everything except maths and science. They are univeral constants, they are things which transend cultures, languages and geography because they are somehow external to us.
QUOTE (magpies+Aug 5 2009, 11:13 PM)
it is impossible to use an infinitely large number in math without making the problem give the answer you want it to give
Oh really? So you can tell me if there's a bijection between the integers and the rational numbers then, both of whom are infinitely large sets. What about the rationals and the irrationals?
Just because your very narrow experience of mathematics is laughable doesn't mean it's the limits to mathematics in actuality. Look up cardinality and Cantor.
Religion? Belief without any idea how the universe works?
Just because you don't and can't understand it, doesn't mean it's wrong. It just means you're stupid.
Just because your very narrow experience of mathematics is laughable doesn't mean it's the limits to mathematics in actuality. Look up cardinality and Cantor.
QUOTE (magpies+Aug 5 2009, 11:13 PM)
So... Your wrong. If your not wrong then please show me what infinity looks like by drawing a picture of it. A picture where I dont have to use my mind to make it work. K?
Excellent strawman. I can't draw you a picture of an adjoint operator, doesn't mean they aren't well defined.
Finite set : A set which doesn't have a bijection with a proper subset of itself.
Infinite set : A set which does.
Countably infinite : The cardinality of any set which possesses a bijection with the Natural Numbers
Uncountably infinite : The cardinality of any set with more members than a countably infinite set. Such as the reals. Proof by Cantor's diagonal method.
You and your narrow understanding are not the limits of other people's understanding. Get over yourself.
Finite set : A set which doesn't have a bijection with a proper subset of itself.
Infinite set : A set which does.
Countably infinite : The cardinality of any set which possesses a bijection with the Natural Numbers
Uncountably infinite : The cardinality of any set with more members than a countably infinite set. Such as the reals. Proof by Cantor's diagonal method.
You and your narrow understanding are not the limits of other people's understanding. Get over yourself.
Yes your right humanity will never change its ways im almost in agreement with you on that.
If you want to explain that without useing words like bijection, integers, and irrationals mby even you would understand what your saying... Its not that I don't understand what an integer or irrational number is its just why make something more complicated then it has to be. The answer to your question would be obv if you used simple language. Perhaps that is why you did not? I honestly don't know what bijection means ill go look it up just incase I run into another you some where... See you know your talking to a simpleton as you say yet you still use jargon talk that is the main problem... Do you even know how to take your complicated statements and make them simple enoth for me? I don't understand what is the benefit of talking above others? Is it to keep them out of your circle or did you just not have enoth time to break the complicated words down into 2 or 3 less complicated ones?
If you want to explain that without useing words like bijection, integers, and irrationals mby even you would understand what your saying... Its not that I don't understand what an integer or irrational number is its just why make something more complicated then it has to be. The answer to your question would be obv if you used simple language. Perhaps that is why you did not? I honestly don't know what bijection means ill go look it up just incase I run into another you some where... See you know your talking to a simpleton as you say yet you still use jargon talk that is the main problem... Do you even know how to take your complicated statements and make them simple enoth for me? I don't understand what is the benefit of talking above others? Is it to keep them out of your circle or did you just not have enoth time to break the complicated words down into 2 or 3 less complicated ones?
QUOTE (magpies+Aug 5 2009, 06:22 PM)
Yes your right humanity will never change its ways im almost in agreement with you on that.
If you want to explain that without useing words like bijection, integers, and irrationals mby even you would understand what your saying... Its not that I don't understand what an integer or irrational number is its just why make something more complicated then it has to be. The answer to your question would be obv if you used simple language. Perhaps that is why you did not? I honestly don't know what bijection means ill go look it up just incase I run into another you some where... See you know your talking to a simpleton as you say yet you still use jargon talk that is the main problem... Do you even know how to take your complicated statements and make them simple enoth for me? I don't understand what is the benefit of talking above others? Is it to keep them out of your circle or did you just not have enoth time to break the complicated words down into 2 or 3 less complicated ones?
Each word is a concept in itself. If he spelled out what each term meant, his post would be 12 times longer, and you would have been 12 times less likely to read it.
You obviously have no interest in learning, so why are you on this forum?
If you want to explain that without useing words like bijection, integers, and irrationals mby even you would understand what your saying... Its not that I don't understand what an integer or irrational number is its just why make something more complicated then it has to be. The answer to your question would be obv if you used simple language. Perhaps that is why you did not? I honestly don't know what bijection means ill go look it up just incase I run into another you some where... See you know your talking to a simpleton as you say yet you still use jargon talk that is the main problem... Do you even know how to take your complicated statements and make them simple enoth for me? I don't understand what is the benefit of talking above others? Is it to keep them out of your circle or did you just not have enoth time to break the complicated words down into 2 or 3 less complicated ones?
Each word is a concept in itself. If he spelled out what each term meant, his post would be 12 times longer, and you would have been 12 times less likely to read it.
You obviously have no interest in learning, so why are you on this forum?
QUOTE
And you fail to realize if we didnt have math and physics we would have some thing in its place and a much better some thing at that.
Religion? Belief without any idea how the universe works?
Just because you don't and can't understand it, doesn't mean it's wrong. It just means you're stupid.
First off I can't believe each of thouse "concepts" would take 12 times as many words to explain... probably only 5 at max per what 4 words? thats like 20 extra words to make what your saying understandible to everyone vs having it only understood by thouse that are like you... I guess if you want to be cryptic I cant stop you.
As for learning I do have interest in learning but I would like it to be some thing I don't already understand. So I guess im just here hoping someone has some concept I dont understand. Of course if they use vague or cryptic language I will have to work harder to understand what they are saying...
As to alexg of course your right it doesnt make a difference if I understand some part of the world that works it will still work. However its not the part of the world works thats causing my stupidity in this case. Its the terms being used. The world is built on sound logic the meaning of words is less so.
As for learning I do have interest in learning but I would like it to be some thing I don't already understand. So I guess im just here hoping someone has some concept I dont understand. Of course if they use vague or cryptic language I will have to work harder to understand what they are saying...
As to alexg of course your right it doesnt make a difference if I understand some part of the world that works it will still work. However its not the part of the world works thats causing my stupidity in this case. Its the terms being used. The world is built on sound logic the meaning of words is less so.
magpies,
Here is the article on the word "bijection": Bijection. Please read this over and then describe Bijection in 5 words. If you can accomplish this, we will make a bigger effort to explain technical terms to you.
Here is the article on the word "bijection": Bijection. Please read this over and then describe Bijection in 5 words. If you can accomplish this, we will make a bigger effort to explain technical terms to you.
Ok so bijection from what I took from wiki in terms of what alpha could have said...
...Alpha said...
So you can tell me if there's a bijection between the integers and the rational numbers then
...He could have said...
So you can tell me if there's a point where integers and the rational numbers meet then?
So to describe a bijection in this case I could say the one place where sets meet. About 5 words right?
...Alpha said...
So you can tell me if there's a bijection between the integers and the rational numbers then
...He could have said...
So you can tell me if there's a point where integers and the rational numbers meet then?
So to describe a bijection in this case I could say the one place where sets meet. About 5 words right?
magpies,
No, the new sentence no longer has the same meaning. If you abbreviate concepts, you lose meaning. Because of this, we must use technical terms to express complex subjects.
My abbreviation of "bijection" is as follows:
A case where every value in one set has a unique corresponding value in another set.
I count 16 words.
No, the new sentence no longer has the same meaning. If you abbreviate concepts, you lose meaning. Because of this, we must use technical terms to express complex subjects.
My abbreviation of "bijection" is as follows:
A case where every value in one set has a unique corresponding value in another set.
I count 16 words.
A case where every value in one set has a unique corresponding value in another set.
Ok so let me see what I can do with this to make it shorter if thats the goal...
Dont need to say a case. Instead of saying one set and another set you could just say sets. That gets rid of about 6 words...
Anyhow... Thanks you made it alot simpler now I get what your talking about and I didn't even have to read a bunch of wiki just to figure it out. Do you understand why talking in a simpler way benefits the conversation between you and someone who is not as complex?
As to alphas question... There are technicaly equal amounts of any type of number but if you are going from a scale of say 1 to 10 the numbers 1-2-3 thru 10 are not going to be as vast as the decimal placed numbers in that example. Because there are infinite decimal numbers in between 1-2 where as you only have 10 whole numbers.
Ok so let me see what I can do with this to make it shorter if thats the goal...
Dont need to say a case. Instead of saying one set and another set you could just say sets. That gets rid of about 6 words...
Anyhow... Thanks you made it alot simpler now I get what your talking about and I didn't even have to read a bunch of wiki just to figure it out. Do you understand why talking in a simpler way benefits the conversation between you and someone who is not as complex?
As to alphas question... There are technicaly equal amounts of any type of number but if you are going from a scale of say 1 to 10 the numbers 1-2-3 thru 10 are not going to be as vast as the decimal placed numbers in that example. Because there are infinite decimal numbers in between 1-2 where as you only have 10 whole numbers.
I appreciate the time and effort that you have given to this exercise. I understand that the use of technical terms is confusing to someone who doesn't know their meaning, but the problem is that no-one has the time or energy to explain every technical detail when they are discussing a topic. If I or anyone else here was being paid to explain these concepts, we would be happy to explain each and every term, but we're not. Because of this, I must ask you to do a little extra work and look up words that you don't understand before rejecting an idea.
Thank you for listening.
Thank you for listening.
Thanks I guess I can only ask the same of you to take some time when talking to me or someone else you think might not be as advanced.
In trigonometry
1/0 is undefined
and
0/1 is zero
then 0/0 is 1
if zero divided by zero is not one prove it
hehe.
1/0 is undefined
and
0/1 is zero
then 0/0 is 1
if zero divided by zero is not one prove it
hehe.
QUOTE (magpies+Aug 6 2009, 12:22 AM)
If you want to explain that without useing words like bijection, integers, and irrationals mby even you would understand what your saying... Its not that I don't understand what an integer or irrational number is its just why make something more complicated then it has to be.
Personally I don't think you understand those words. And I use those words because they have precise definitions, they have clear well defined meanings. You're basically saying "Stop using clear, unambigious language because it's over my head". I don't ask doctors to stop using complicated terms because I don't understand them. Why? Because I know they do and I know they have such terminology as a means of speeding their information exchanges. That's the point of any terminology, to convey complicated concepts quickly, to those familiar with them.
Personally I don't think you understand those words. And I use those words because they have precise definitions, they have clear well defined meanings. You're basically saying "Stop using clear, unambigious language because it's over my head". I don't ask doctors to stop using complicated terms because I don't understand them. Why? Because I know they do and I know they have such terminology as a means of speeding their information exchanges. That's the point of any terminology, to convey complicated concepts quickly, to those familiar with them.
QUOTE (magpies+Aug 6 2009, 12:22 AM)
. The answer to your question would be obv if you used simple language. Perhaps that is why you did not? I honestly don't know what bijection means ill go look it up just incase I run into another you some where... See you know your talking to a simpleton as you say yet you still use jargon talk that is the main problem... Do you even know how to take your complicated statements and make them simple enoth for me? I don't understand what is the benefit of talking above others? Is it to keep them out of your circle or did you just not have enoth time to break the complicated words down into 2 or 3 less complicated ones?
So you claim mathematics using zero or infinity is nonsense but you admit you're unfamiliar with what are to any mathematician basic concepts? Bijections are something you learn about before you even go to uni to do maths.
Are you seriously telling me you don't see the point in technical terminology? Don't see any benefit for doctors using special terms rather than "He's got a dark squidgy thing on that bone in his back"? Don't see any benefit for police to use "Code 214, situation green" rather than a long winded explaination and description? Don't see any benefit in mechanics saying "crank shaft" rather than "that long spinning thing in the middle"?
Besides, you implied you had some great grasp of what was and wasn't valid mathematics and I basically asked you to put up or shut up using 1st year terminology. The words I used are not 'high brow', they are stuff plenty of 1st years learn about and might even know before they get to uni. If you don't want to have people talk over your head, don't try to make it seem like you've got some amazing grasp of what is or isn't valid in their area of work. I don't go into a doctors and say "Don't bother testing for cancer, obviously it's not!". Why? Because I'm not a doctor, I have no medical training, I hav only basic biology knowledge. You tried to make claims about mathematics when you have no mathematical knowledge and you're whining I talked over your head?!
And this is just a 1st year concept. If I were talking about something from a 3rd or 4th year course there'd be so many terms which needed definition it's pointless to try. In one word, say 'holonomy', you can convey a huge amount of information. That's what terminology is for.
Are you seriously telling me you don't see the point in technical terminology? Don't see any benefit for doctors using special terms rather than "He's got a dark squidgy thing on that bone in his back"? Don't see any benefit for police to use "Code 214, situation green" rather than a long winded explaination and description? Don't see any benefit in mechanics saying "crank shaft" rather than "that long spinning thing in the middle"?
Besides, you implied you had some great grasp of what was and wasn't valid mathematics and I basically asked you to put up or shut up using 1st year terminology. The words I used are not 'high brow', they are stuff plenty of 1st years learn about and might even know before they get to uni. If you don't want to have people talk over your head, don't try to make it seem like you've got some amazing grasp of what is or isn't valid in their area of work. I don't go into a doctors and say "Don't bother testing for cancer, obviously it's not!". Why? Because I'm not a doctor, I have no medical training, I hav only basic biology knowledge. You tried to make claims about mathematics when you have no mathematical knowledge and you're whining I talked over your head?!
QUOTE
...Alpha said...
So you can tell me if there's a bijection between the integers and the rational numbers then
...He could have said...
So you can tell me if there's a point where integers and the rational numbers meet then?
Nonsense. That sentence shows you don't grasp what the word means. A bijection is a map which is both injective and surjective. Injective means every element in the range has one or less preimages and surjective means every element in the range has one or more preimages. A bijection means there's relation between each element of a domain to one and only one element of the range. If there's a bijection between the integers and the rationals that means you can construct an invertible function such that you can associated with each and every rational one and only one integer (and thus vice versa). Of course now you need to know what domain and range mean.So you can tell me if there's a bijection between the integers and the rational numbers then
...He could have said...
So you can tell me if there's a point where integers and the rational numbers meet then?
And this is just a 1st year concept. If I were talking about something from a 3rd or 4th year course there'd be so many terms which needed definition it's pointless to try. In one word, say 'holonomy', you can convey a huge amount of information. That's what terminology is for.
QUOTE (magpies+Aug 6 2009, 02:17 AM)
As to alphas question... There are technicaly equal amounts of any type of number but if you are going from a scale of say 1 to 10 the numbers 1-2-3 thru 10 are not going to be as vast as the decimal placed numbers in that example. Because there are infinite decimal numbers in between 1-2 where as you only have 10 whole numbers.
Wrong.
There's infinitely many rational numbers between any integer but the cardinality of the sets is equal. There's infinitely many irrational numbers between any integer but the cardinality of the irrationals is strictly larger than the rationals or integers.
Wrong.
There's infinitely many rational numbers between any integer but the cardinality of the sets is equal. There's infinitely many irrational numbers between any integer but the cardinality of the irrationals is strictly larger than the rationals or integers.
I just happened to have this question pop in my head and by reading the posts it made me realize my lack of mathematical knowledge(especially terminology) and question zero itself.
Is zero a number?
With that thought I justified in my own mind why I was told that I could not.
-You cannot divide a non-number by a non-number to obtain a number.
-You cannot divide a number by a non-number.
Edit: I obtained this thought with a light versus shadows analogy.
Is zero a number?
With that thought I justified in my own mind why I was told that I could not.
-You cannot divide a non-number by a non-number to obtain a number.
-You cannot divide a number by a non-number.
Edit: I obtained this thought with a light versus shadows analogy.
Zero is like infinity you are right is far more a concept then a number.
[Moderator: Suspended 30 days for lying and for claiming he himself does not belong on this forum.]
[Moderator: Suspended 30 days for lying and for claiming he himself does not belong on this forum.]
If 0=1-1 and 0= infinity - infinity, then 0 can refer to either the absence of a singularity OR the absence of everything. Assuming that infinity represents infinite singularities, then the absence left by infinite singularities could be divided into the absence left by one singularity and infinite number of times. Therefore:
0/0 = 1, infinity, and/or anything in between depending on the specific absence in question - assuming absences exist in the image of whatever it was that was subtracted to create them.
[Moderator: Banned 15 days for being completely worthless.]
0/0 = 1, infinity, and/or anything in between depending on the specific absence in question - assuming absences exist in the image of whatever it was that was subtracted to create them.
[Moderator: Banned 15 days for being completely worthless.]
QUOTE (light in the tunnel+Oct 3 2009, 06:01 PM)
If 0=1-1 and 0= infinity - infinity, then 0 can refer to either the absence of a singularity OR the absence of everything. Assuming that infinity represents infinite singularities, then the absence left by infinite singularities could be divided into the absence left by one singularity and infinite number of times. Therefore:
0/0 = 1, infinity, and/or anything in between depending on the specific absence in question - assuming absences exist in the image of whatever it was that was subtracted to create them.
How many times can you reach into an empty box and bring out 0 marbles? As many times as you want, right? That's why 0/0=undefined; it can be anything, including 0 and infinity.
0/0 = 1, infinity, and/or anything in between depending on the specific absence in question - assuming absences exist in the image of whatever it was that was subtracted to create them.
How many times can you reach into an empty box and bring out 0 marbles? As many times as you want, right? That's why 0/0=undefined; it can be anything, including 0 and infinity.
QUOTE (Ainulph+Oct 3 2009, 03:21 AM)
I just happened to have this question pop in my head and by reading the posts it made me realize my lack of mathematical knowledge(especially terminology) and question zero itself.
Is zero a number?
With that thought I justified in my own mind why I was told that I could not.
-You cannot divide a non-number by a non-number to obtain a number.
-You cannot divide a number by a non-number.
Edit: I obtained this thought with a light versus shadows analogy.
This is incorrect, the IEEE floating point standard specifies:
NaN/NaN=indeterminate
Number/NaN=NaN
NaN/Number=NaN
Is zero a number?
With that thought I justified in my own mind why I was told that I could not.
-You cannot divide a non-number by a non-number to obtain a number.
-You cannot divide a number by a non-number.
Edit: I obtained this thought with a light versus shadows analogy.
This is incorrect, the IEEE floating point standard specifies:
NaN/NaN=indeterminate
Number/NaN=NaN
NaN/Number=NaN
Of course floating point numbers are not "numbers" in the mathematical sense.
This is because there are billions of IEEE numbers such that
(1 + x) = 1
While for math numbers, this is not the case for any x except zero.
So the IEEE definitions of operations which may be (some of my professors would disagree) convenient for engineers and are certainly convenient for chip designers, bear only approximate relation to math operators.
This is because there are billions of IEEE numbers such that
(1 + x) = 1
While for math numbers, this is not the case for any x except zero.
So the IEEE definitions of operations which may be (some of my professors would disagree) convenient for engineers and are certainly convenient for chip designers, bear only approximate relation to math operators.
QUOTE (flyingbuttressman+Aug 6 2009, 01:02 AM)
magpies,
No, the new sentence no longer has the same meaning. If you abbreviate concepts, you lose meaning. Because of this, we must use technical terms to express complex subjects.
My abbreviation of "bijection" is as follows:
A case where every value in one set has a unique corresponding value in another set.
I count 16 words.
bijection is "a one to one correspondence"
Is that accurate?
although I think that definition would require context to be understood.
No, the new sentence no longer has the same meaning. If you abbreviate concepts, you lose meaning. Because of this, we must use technical terms to express complex subjects.
My abbreviation of "bijection" is as follows:
A case where every value in one set has a unique corresponding value in another set.
I count 16 words.
bijection is "a one to one correspondence"
Is that accurate?
although I think that definition would require context to be understood.
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