How do we know the eternal progression of one infinity doesn't increase at a different rate from the other? In short, I'd argue infinity divided by infinity equals infinity, or perhaps zero.

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You're question raises an interesting point. The idea is that infinity isn't actually a number, it's merely a concept. You cannot prove infinity exists without finite proof of it's definition, and you cannot find finite proof of infinity (infinite).

As infinity does not describe a single number and is always augmenting, it is impossible to claim any viable equation basing itself in the finite definition.

This is merely my analysis of the question by the definition of infinity. However, check out http://www.philforhumanity.com/Infinity_Divided_by... to see the mathematical derivation. According to his logic, which may or may not be flawed (i don't claim to be a mathematician), infinity divided by infinity could equal any positive number, infinity even.

Hope this helps your contemplation.

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I am glad you asked and yes infinity over infinity is not always one............At least as we approach infinity. This is the start of the wonderful world of calculus.

Lets look at a couple of examples:

So you are correct in that one side can approach infinity faster than the other. We call these limits which is nothing more than saying we are getting incrementally close to infinity, zero, or another defined number.

Lets first look at something obvious:

x^2/x------------->infinity/infinity=1 as x approaches infinity right?

No, it approaches infinity.

Conversely x/x^2 approaches zero as x approaches infinity instead of 1.

Now, I know you probably saying hey wait a minute x^2/x=x and x/x^2=1/x. So one is infinity and the other is 1/infinity. Actually the way it is written both would be infinity/infinity but you defined something very important and that is a rate at which the numerator and the denominator approaches infinity. That is the fundamental principle here.

This actually will get quite a bit more advanced and there are many more principles to learn. This is approaching the definition of the fundamental principle of calculus. So to be concise your thesis is that one side will approach infinity faster and that is correct.

I hope this helps.

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Some infinities could be larger than others? :-) Indeterminate.

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Anything divided by itself is equal to unity.

X/X = 1, by definition. When we substitute infinity for X, the answer is still 1.

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