Raphie Frank
excerpt...
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THE MYSTERIOUS ZERO/INFINITY
A new deck of 52 cards usually has two jokers. Likewise there are two jokers that bedevil physics -- zero and infinity. They represent powerful adversaries at either end of the realm of numbers that we use in modern science. Yet, zero and infinity are two sides of the same coin -- equal and opposite, yin and yang. "Multiply zero by anything and you get zero. Multiply infinity by anything and you get infinity. Dividing a number by zero yields infinity; dividing a number by infinity yields zero. Adding zero to a number leaves the number unchanged. Adding a number to infinity leaves infinity unchanged." Yet, the biggest questions in science, philosophy, and religion are about nothingness and eternity, the void and the infinite, zero and infinity.
http://www.fmbr.org/editoral/edit01_02/edit6_mar02.htm
=============================================================

IF 0 and infinity are indeed two sides of the same coin, as, for instance, Charles Seife posits in:

Zero: The Biography of a Dangerous Idea
http://www.amazon.com/Zero-Biography-Dange...e/dp/0140296476

...then how is it we seem to treat these two entities so differently?

If we can speak of 0 + 1, then why not infinity - 1?

For myself, in order not to run afoul of scientific dogmas worthy of 17th Century Italy, I have taken to referencing "infinity" by using the term "Z" to denote "virtual infinity," a number as big as the mind can imagine at any given point in time, a number so big, in fact, that it falls just this side shy of being a "concept."

And the flip side of Z?

NOT ZERO.

Because 0 is not just "virtual nothing" but actual nothing. In other words, I would posit, the flip side of... infinity. Yet, while the one is considered a number, the other is considered a "concept." To my way of thinking, this creates a false "apples vs. oranges" thought scenario that hinders rational analysis.

Thoughts?

Best,
Raphie

P.S. THE STANDARD VIEW(S)

==============================================================

Is zero a number?
------------------------
The simple answer: Yes, of course zero is a number. (I'm giving you the benefit of the doubt and not saying, "you dolt.") What, you think it's maybe an animal or vegetable?

The mathematical answer: Well, it depends on what you mean by "number." This is not sarcasm, there are different sets of numbers that build up to the Real Number system (the unique complete ordered field).

Zero is clearly an element of the set of Real Numbers, it's the "additive identity" -- the number that, when added to any other number x, doesn't change the value of x. (Similarly, 1 is the multiplicative identity -- the number that, when multiplied by any other number x, doesn't change the value of x.) Thus, zero is a number, just as any other element of the set of Real Numbers is a number.

==============================================================

What is infinity?
------------------------

Infinity is not a number; it is the name for a concept. Most people have sort of an intuitive idea of what infinity is - it's a quantity that's bigger than any number. This is sort of correct, but it depends on the context in which you're using the concept of infinity (see below).

There are no numbers bigger than infinity, but that does not mean that infinity is the biggest number, because it's not a number at all. For the same reason, infinity is neither even nor odd.

MORE: http://mathforum.org/dr.math/faq/faq.large.numbers.html
==============================================================
Ivars
0 is a place where direction changes. In numbers, sign changes at 0. It is a place /point of reference, not a number.

If we would speak of + 100% as positive, - 100% as negative, there might be various mixes with fractal + or - sign ( not 100%) based direction relative to reference point.

Reference point itself, and movement along it ( if we have a plane divided in 2 parts by 0 reference line) is then NEUTRAL (neither positive, nor negative).

The same is e.g infinity in projective geometry. It does not have sign, but at infinity direction changes. Infinity is another NEUTRAL reference place in projective geometry. Movement in or along 0 line ir line at infinity is sign neutral.

So in projective geometry there are 2 places where direction (number signs ) change- at 0 ( origin) and infinity.
rpenner
Is Zero a number? Yes.
Proof:
Let x be a number. x - x = 0. 0*x = (x - x)*x = x² - x² = 0. x + 0 = x + (x - x) = 2 x - x = (2-1)x = 1x = x = x1 = x(1 - 1 + 1) = (x - x) + x = 0 + x.
So if x is a number, then 0 would seem to have to be a number or your arithmetic is going to go all wonky.

And all numbers are concepts.
sporacle
Wonderful question, Ralphie.

Numbers, like 1, 2, 3 etc maintain specific identity and sets of operations we do with them also maintain identity and are obviously useful. Personally I think numbers are integral with every aspect of reality.

It’s interesting that very early mathematicians didn’t use zero for a long time. Most people still think zero is nothing and could not be a part of anything or interrelated with anything. At least zero is a concept and it’s used in mathematics, whether people think it is something or not.

Infinity is at least a concept. A long time back many people said God (or whatever they thought was in charge of all reality) is infinite or somehow without limit. And along the way no doubt somebody kept multiplying or dividing until they realized it would keep going forever and just put the name on it.

Sets of mathematical operations we use often have solutions that range from zero to infinity, but the ones between the limits we assign are sure useful. Most people just use them and ignore what zero and infinity may mean.

Betcha zero and infinity are the same. Maybe you’ve seen my yammering about an unlimited entity elsewhere. One entity from no identity (zero) to infinite identity.

Best wishes

Sporacle
Raphie Frank
QUOTE (rpenner+Mar 25 2009, 04:37 PM)
Is Zero a number? Yes.
Proof:
Let x be a number. x - x = 0. 0*x = (x - x)*x = x² - x² = 0. x + 0 = x + (x - x) = 2 x - x = (2-1)x = 1x = x = x1 = x(1 - 1 + 1) = (x - x) + x = 0 + x.
So if x is a number, then 0 would seem to have to be a number or your arithmetic is going to go all wonky.

And all numbers are concepts.

I agree with you in the most general sense.

Zero, for me, is a "number" AND a "concept" ( as are all numbers). Infinity, on the other hand is only a concept. As unorthodox as my views may be, I would like to publicly assert that I do, indeed, recognize that zero, at least according to accepted axioms, is a provable number, while infinity is not.

Best,
RF
AlphaNumeric
Raphie, rather than doing stupid numerology, why don't you bother to look up what the construction of the Real numbers is? Then you wouldn't be wasting your time with pseudo-philisophical BS like this. If you want to construct a ring or a group then you need certain properties for consistency.

Definition of a group G :

1. G possesses a binary operation # such that if a and b are in G a#b is too.
2. There is an e in G such that for any a in G a#e = e#a = a.
3. Given any a in G there's a b such that a#b = b#a = e
4. (a#b)#c = a#(b#c) for all a,b,c in G

This is the formal definition of a group, I've made no mention of actual numbers because groups are a much wider concept than just everyday numbers. However, the Reals are a group under addition. This is obvious when I rephrase the group definitions in terms of numbers,

1. The real numbers have a binary operation +, such that given real number a and b, a+b is another real number.
2. The reals have 0 such that 0+a = a+0 = a for all a in the reals.
3. For any a in the reals there's -a such that a+(-a) = (-a)+a = 0.
4. (a+b)+c = a+(b+c)

So zero is an essential entity for the consistency of addition on numbers. Similar derivations exist for rings (which the Reals are) and fields (which the Reals are). Why don't you actually open a book on basic number theory rather than pissing about with n'th formulae which you can't even analyse algebraicly?
H2O
If you think of numbers as a quantity of something then 0 is a number. When you run out of that something (quantity of nothing) then you have 0 of that something.

Just a thought...
magpies
Infinity is just a concept that can never be understood. While zero is an understanding that can never be conceptualized.

Zero is a number but imo has no real practical use. I tend to question maths with zeros in it as being valid or at the very least not simplifyed enoth.
NoCleverName
QUOTE (magpies+Apr 8 2009, 06:34 AM)
Zero is a number but imo has no real practical use. I tend to question maths with zeros in it as being valid or at the very least not simplifyed enoth.

Nice try at trolling. No one will bite, however.
magpies
Not that I was trolling but you seem to have if I was...

So I take it your in the camp that thinks division by zero is ok?
H2O
Division by 0 is ok. Why wouldn't it? As far as I can tell it signifies the impossible, my example being calculating the energy required to accelerate a mass to the speed of light. I can't remember the equation off hand but I do remember that if you put in the speed of light as the goal velocity and you put in a mass other than 0 then you end up with x/0 = E. Thus it takes an infinite amount of energy to accelerate a mass (x) to the speed of c.

Although I am sure that dividing by 0 signifies other things (not just the impossible) depending on where the numbers come from and how you got there.
Kaeroll
QUOTE (H2O+Apr 9 2009, 01:34 PM)
Division by 0 is ok. Why wouldn't it? As far as I can tell it signifies the impossible, my example being calculating the energy required to accelerate a mass to the speed of light. I can't remember the equation off hand but I do remember that if you put in the speed of light as the goal velocity and you put in a mass other than 0 then you end up with x/0 = E. Thus it takes an infinite amount of energy to accelerate a mass (x) to the speed of c.

Although I am sure that dividing by 0 signifies other things (not just the impossible) depending on where the numbers come from and how you got there.

There was a detailed discussion of this recently on here. Division by zero is undefined, signifying nothing at all.

Raphie Frank
QUOTE (Kaeroll+Apr 9 2009, 01:40 PM)
Division by zero is undefined, signifying nothing at all.

To state that division by zero is undefined and to state that it signifies nothing at all are two very different, well, uh... concepts. Depending on how one looks at it, division by 0 can signify either everything or nothing.

A.
0*x = 0

The set of all solutions for x is infinite.

B.
0*x = some number not equal to 0

The set of all solutions for x is the null set.

Algebraically A. corresponds with 0/0 while B. corresponds with 0/x such x is > or < 0

The point being that there are at least two distinct "flavors" or cases one runs across when dividing by zero, one case when the numerator is 0 and one when it is not 0. If division by 0 truly signified "nothing at all," one might easily argue that it should matter not a whit that nature of the numerator.

Best,
Raphie
Euler
After all the explanations, you still don't get it. Wow, just wow.
Raphie Frank
QUOTE (Euler+Apr 9 2009, 02:38 PM)
After all the explanations, you still don't get it. Wow, just wow.

You are too funny Euler. That </edit> division by 0</> is undefined is NOT in question. It is the nature of that lack of definition that is. And since this is a thread about 0 the concept as well as 0 the number, I will ask you politely (yet again) to refrain from tossing around insults, implied or otherwise.

Best,
Raphie
Euler
QUOTE (Raphie Frank+Apr 9 2009, 02:51 PM)
That 0 is undefined is NOT in question. It is the nature of that lack of definition that is.

And now you think 0 is undefined? This just gets better and better.

Do you actually know any mathematics?
Raphie Frank
QUOTE (Euler+Apr 9 2009, 02:57 PM)
And now you think 0 is undefined? This just gets better and better.

Do you actually know any mathematics?

Euler, you really might wish to think about taking up a second career as a sleazy reporter who quotes out of context. In any case, thank you for pointing out the typo. I went back and edited my previous post to read "division by zero."
Raphie Frank
QUOTE (Raphie Frank+Apr 9 2009, 02:13 PM)
To state that division by zero is undefined and to state that it signifies nothing at all are two very different, well, uh... concepts. Depending on how one looks at it, division by 0 can signify either everything or nothing.

A.
0*x = 0

The set of all solutions for x is infinite.

B.
0*x = some number not equal to 0

The set of all solutions for x is the null set.

Algebraically A. corresponds with 0/0 while B. corresponds with 0/x such x is > or < 0

The point being that there are at least two distinct "flavors" or cases one runs across when dividing by zero, one case when the numerator is 0 and one when it is not 0. If division by 0 truly signified "nothing at all," one might easily argue that it should matter not a whit that nature of the numerator.

Best,
Raphie

And what I mean by "out of context" is that the topic of discussion was "division by zero." It was plain and obvious to, I imagine, just about anyone but you.
Euler
Given your complete lack of mathematical competency, it is impossible for me to identify genuine typos. I'm not convinced yours was.
QUOTE (Raphie Frank+Apr 9 2009, 03:06 PM)
That </edit> division by 0</> is undefined is NOT in question. It is the nature of that lack of definition that is.

If you think you can question "the lack of definition", then you have not understood the countless explanations we have provided you with. Please, do continue to dig your hole.
Raphie Frank
QUOTE (Euler+Apr 9 2009, 03:11 PM)
If you think you can question "the lack of definition", then you have not understood the countless explanations we have provided you with. Please, do continue to dig your hole.

It would be great fun to listen in on, if it were possible, the dialogue between a 17th Century mathematician and a 19th Century mathematician on the topic of Grandi's series. However, since it is not possible, such a thought in and of itself constitutes, I guess, an illogical absurdity...

GRANDI'S SERIES
The infinite series 1 - 1 + 1 - 1 + …
=============================================================
Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:

S = 1 - 1 + 1 - 1 + …, so
1 - S = 1 - (1 - 1 + 1 - 1 + …) = 1 - 1 + 1 - 1 + … = S,

resulting in S = 1/2. The same conclusion results from calculating -S, subtracting the result from S, and solving 2S = 1.[1]

The above manipulations do not consider what the sum of a series actually means. Still, to the extent that it is important to be able to bracket series at will, and that it is more important to be able to perform arithmetic with them, one can arrive at two conclusions:

The series 1 - 1 + 1 - 1 + … has no sum.[2][1]
...but its sum should be 1/2.[2]

In fact, both of these statements can be made precise and formally proven, but only using well-defined mathematical concepts that arose in the 19th century. After the late 17th-century introduction of calculus in Europe, but before the advent of modern rigor, the tension between these answers fueled what has been characterized as an "endless" and "violent" dispute between mathematicians.[3][4]

http://en.wikipedia.org/wiki/Grandi's_series
=============================================================
Euler
Oh no! This makes you look even more ignorant of mathematics! Latter day mathematicians would be fall upon strange, paradox-like situations because no one had rigorously defined and constructed the mathematical objects in question.

Since then, mathematicians have carefully developed topics like real analysis, within which falls the construction of the real numbers. The reals are the unique Dedekind-complete ordered field. A mathematician knows this, and knows how the reals are defined. Because of this, a mathematician does not ask "how do you divide by zero", in the same sense that he does not ask "how do you boil a 12". It's not "unexplored mathematics" (mathematicians actually love that kind of thing), it's simply a question asked by someone who doesn't understand what the real numbers are (for example, Raphie Frank).

Come on, put your foot in your mouth again. This is becoming fun.
sporacle
You seem to know mathematics, Euler. Here is a naive question and should be easy for you. Is dx=0 real?
rpenner
QUOTE (sporacle+Apr 23 2009, 03:18 AM)
You seem to know mathematics, Euler.  Here is a naive question and should be easy for you.  Is dx=0 real?

No, you ignoramus. It's an equation. And since the author of the equation has the responsibility of explaining the terms and the relevant universe of discourse, you have failed in your responsibilities.

Therefore you are ruled a irresponsible derelict, incapable of meaningful discourse. But, hey, you win an invitation to the May Day party. There will be pizza. More details to be announced.
Raphie Frank
QUOTE (rpenner+Apr 23 2009, 08:18 AM)
s... ince the author of the equation has the responsibility of explaining the terms and the relevant universe of discourse, you have failed in your responsibilities.

The gauntlet has been laid, sporacle. How about responding ro RPenner's challenge?

Best,
RF
Raphie Frank

"since the author of the equation has the responsibility of explaining the terms and the relevant universe of discourse..."

This statement implies that the ONCE IN A ZILLION genius would be "wrong" simply for evidencing lack of clarity in the eyes of the merely "extraordinary"...

Hmmm... - RF
rpenner

a=bc=cd/e²

Which is to high precision correct except for having no context for the reader at all.
Beer w/Straw

F=MLT^-2

Bored.
Derek1148
QUOTE (Raphie Frank+Apr 23 2009, 09:14 AM)
The gauntlet has been laid...

Hey, shouldn't it be: "The gauntlet has been thrown down."
sporacle
QUOTE (rpenner+Apr 23 2009, 08:18 AM)
No, you ignoramus. It's an equation.
you are ruled a irresponsible derelict, incapable of meaningful discourse.

As I said, a NAIVE question. If I read you correctly, you said that dx= 0 is not real, it's an equation. Do you mean that equations are not real? Is the mental process of using symbolic operations (including thinking about zero) not real?

I guess judgment has been passed on spo. But I haven't been arrested and will still speak if I have something to say.
joestaley
I have a new theory of Zero Numbers which vastly expands the concept of zero, as well as all mathematics (eg. The Real Numbers, Algebra, etc.) which uses zero.
It is posted on a website at [Moderator: Web site link deleted because this is a Discussion forum. So discuss, please, don't spam/advertise without discussion/solicit. Thank you.]
Thank you
Joe Staley
boit
Something can be imagined to be infinitely big or infinitely small.
Any iteration that goes on and on can be said to be an infinite operation.
There is a Hebrew letter resembling`N, that denotes approachable infinity
I know for sure zero is a number. It is an even number (add an even number to an odd number any you get an odd number)
Knowledge of zero as a number came much later. It was only recognized only as a place holder (a necessity to make computation easy, much like when we say let the value of something be x).
Have I done my homework well?
kowalskil
QUOTE (Raphie Frank+Mar 26 2009, 08:29 AM)
I agree with you in the most general sense.

Zero, for me, is a "number" AND a "concept" ( as are all numbers). Infinity, on the other hand is only a concept. As unorthodox as my views may be, I would like to publicly assert that I do, indeed, recognize that zero, at least according to accepted axioms, is a provable number, while infinity is not.

Best,
RF

Yes, infinity is a concept and zero is an unusual number.

Ludwik Kowalski (see Wikipedia)
http://csam.montclair.edu/~kowalski/life/intro.html
LaurieAG
If you divided by zero in the Windows 98a calculator the answer you would receive was 'error: negative infinity' (sometimes positive infinity). In the Windows 98b calculator the answer was changed to 'error: cannot divide by zero'.
Blu3dud3
Wouldnt You Include 0 as a actual Number?
Considering WE use the terms Absolute 0 and in most references we say there is 0 possible solutions.

0 Can also be used as a concept as i hear in a lot of mathematical terms of its approaching 0 ( so its like a concept of reaching infinity )

Take X^2 for example, it keeps going until it reaches infinity ( A mathematical concept )

Or When you use P = E^RT Its exponentially growing to infinity ( A concept ) Or when using as Decay It keeps getting smaller and smaller until it reaches 0 ( Which would be signified as until it reaches nothing ? )
VioletSilence
Guys,

I would say:

A= 0,A = 1,A = 2,A =3,A=4,A=5,A=6,A=7,A=8,A=9 ,A = Infinity when A0 to A9 are equal and IF Degree of “A” spin between 0-360 Degrees in X,Y,Z plane, Clockwise and counterclockwise respectively."A" will be equal to infinity when it heads outside any of these planes regardless of its direction.

Let’s spin the letter A in an interval of 45 degrees, this will generate Number 1 to 8,( for transmission from zero to “the end (9)” we only need to spin 180 degree), that is what make these two numbers identical to the others, they are representing start and the end .They are in and outside of a two dimensional plane.

Now What would you say to that?!! User posted image: http://www.spacetectonic.com/aine.html
Robittybob1
tonydisalva - posts make no sense to me at all. Sorry
Mekigal
QUOTE (tonydisalva+Jan 5 2013, 11:06 AM)
Hello
I will discs about the Zero a number is most conceptional number in details