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Is there a Mathematical Proof that
I do not believe that it is true, so is there a proof?

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Is there a Mathematical Proof that
James S Saint
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Posted 10/31/09 - 11:32 AM:
Subject: Is there a Mathematical Proof that 		quote post
#1
While considering how the universe came to be, I ran into a problem in mathematics involving infinities and zeroes. I have put together a means for correcting the problem, but before I get into that, I would like to ask;

I do not believe that it is true, so is there a proof that "inf * 0 = 0"?

Edited by unenlightened on 11/02/09 - 08:11 AM
To Mega Therion
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Posted 10/31/09 - 11:56 AM:
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Infinity times zero is an undefined expression; to make sense of it you would have to specify the exact expression that becomes infinity times zero as you go to the limit, and solve the limit in the standard way.
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Posted 11/01/09 - 07:23 PM:
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Anybody want to address the question itself?

I think you can come up with some assumptions about the behavior of an infinite quantity, but only by using limits, since infinity is not a simple plug-in quantity. You also need to be careful that there may be multiple answers.

So, when you say, "inf*0", you really mean, lim(x*0), as x approaches infinity. You can see this on the graph, y = x*0, that the limit would appear to be zero.

Edited by unenlightened on 11/02/09 - 08:05 AM
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James S Saint
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Posted 11/02/09 - 05:07 AM:
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swstephe wrote:
Anybody want to address the question itself?

I think you can come up with some assumptions about the behavior of an infinite quantity, but only by using limits, since infinity is not a simple plug-in quantity. You also need to be careful that there may be multiple answers.

So, when you say, "inf*0", you really mean, lim(x*0), as x approaches infinity. You can see this on the graph, y = x*0, that the limit would appear to be zero.


This seems to be the sane response.

In discussions with professional mathematicians, they admit that at times they use it to equate to 0 and at times they used it as indeterminate and even at times relegate it to being undefined.

The issue is really about the cardinality of both the infinity in question and the zero. It depends on just how you got to the point of needing to know the answer.

Philosophically, this is another example of how often, in all fields, there is not really a direct question to answer correlation for all questions. It depends on how you got to the question as to which answer is really appropriate or even accurate.

This is one of the aberrant effects of a mind as it lustfully or lazily seeks a simple answer to any question, then often presumes to attack others in proclamation that they must not know.

Sometimes, often times, one is not really qualified to ask the question.

Edited by James S Saint on 11/02/09 - 11:26 AM
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Posted 11/02/09 - 06:44 AM:
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Anything times zero equals zero.

Zero is a set definer hence 10 is one set of ten, 100 is one set of ten sets of ten etc. Otherwize it is binary sets of 2 and 10 is one set of 2, 100 is one set of two sets of two etc.

infinity x 0 = 0 , but infinity0 is an infinite number of sets of 10. (Base 10).

Is there some definition to that expressed numerically? If the notion the numbers described was discerned perhaps it would stretch beyond the mathematical definion.

Edited by unenlightened on 11/02/09 - 08:10 AM
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Posted 11/02/09 - 02:57 PM:
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You can run the N(n-1) system.

Essentially arguing that X = 0 because X = ab where both a*0 and b*0 = 0


But this is still flawed.. If you want try understanding what I wrote in the brick system.

Infinity cannot be treated as a mere rational number. As such the equation looks like:

iX = i(ab) = i0

Or in other words infinity * 0 = the irrational integer 0.
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Posted 11/02/09 - 07:45 PM:
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You have to be careful with "infinity" it means, simply, "no limit". It can't be treated as a normal number with "cardinality". To show you what I mean: given a natural number, (within reason*), we can determine certain attributes, such as whether it is "odd" or "even", (divisible by 2), or a prime number, (only evenly divisible by itself and 1). Is "infinity" even or odd? Especially considering that half of infinity is infinity. Is infinity a prime number? Those attributes make it a theoretical point, not a natural number that behaves like other numbers.

* By "within reason", I'm trying to avoid the questions of very large numbers, like Graham's number, whose attributes start to become the territory of real math nerds asking questions like, "do prime numbers stop appearing at some point"?
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James S Saint
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Posted 11/03/09 - 03:39 AM:
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Realize that in calculus, 0 * infinity is used extensively.

iS(x)dx = x

iS(0)dx = 0

But what that is saying is, that the product of 0*dx is being infinitely summed ("iS"). So it is saying that if I multiply 0 times something infinitely small, dx, but then infinitely sum it, I get what I started with, which is fine. But that means;

0 * dx = Y [=0]
iS(Y) = infinity * Y = 0

Thus "inf * 0" is certainly not undefined in all cases and isn't even indeterminate in all cases. What is required is an association between how small of a 0 we have to how large of an infinity we have. This is an issue of cardinality.

In the above example the smallness of dx is assumed to be equal to the greatness of the infinity involved and thus an answer is derivable.

But what that means to me is that if we do not know the cardinality, then the answer is indeterminable, thus;

Inf * 0 = indeterminate

I don't see how it can be anything else.

Edited by James S Saint on 11/03/09 - 03:45 AM
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Posted 11/03/09 - 04:37 AM:
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James S Saint wrote:
Realize that in calculus, 0 * infinity is used extensively.

Really? Can you give a single example? Can you give a single example of a textbook that recommends this?
iS(x)dx = x

iS(0)dx = 0

But what that is saying is, that the product of 0*dx is being infinitely summed ("iS"). So it is saying that if I multiply 0 times something infinitely small, dx, but then infinitely sum it, I get what I started with, which is fine.

But that means;

0 * dx = Y [=0]
iS(Y) = infinity * Y = 0

You just said that "iS" indicates summation, so there is no multiplication in that last line, just summation.
Thus "inf * 0" is certainly not undefined in all cases and isn't even indeterminate in all cases. What is required is an association between how small of a 0 we have to how large of an infinity we have. This is an issue of cardinality.

Even if this is the case, you haven't addressed this issue. Feel free to get to it.

First, though, you should fix your example so that it makes more sense.
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James S Saint
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Posted 11/03/09 - 08:09 AM:
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So you don't believe that "3+3+3+3" is the same as "4 * 3"?

Or that the infinite sum, "3+3+3+3+3...+3", is the same as "infinity * 3"?

An infinite sum in calculus is merely a different way of expressing a particular multiplication of infinity. It is used in relation to an infinitesimal delta, dx, so as to express the relative cardinality of the infinity being used.

So an infinite sum IS an infinite multiplication of the function times the infinitesimal delta.
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