Mathematicians Measure Infinities, Find They’re Equal

Re:Mathematicians Measure Infinities, Find They’re Equal by adenadel on Wednesday September 13, 2017 @05:11PM (#15242728)

This is equivalent to asking what is the average number of digits necessary to represent an arbitrary natural number. If you assume that this is a finite number you can quickly arrive at a contradiction.

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Re:Mathematicians Measure Infinities, Find They’re Equal by zelah on Wednesday September 13, 2017 @05:50PM (#15243051)

So there are natural numbers with an infinite number of digits and that is my point. The average can't be larger than the largest number.

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Re:Mathematicians Measure Infinities, Find They’re Equal by adenadel on Wednesday September 13, 2017 @10:49PM (#15244659)

The only way to reason about this is as a limit.

lim n->infty sum(1..n)/n.

This limit diverges. Your intuition is breaking down. It might be useful for your understanding to study real analysis where these sorts of questions are handled rigorously.

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Re:Mathematicians Measure Infinities, Find They’re Equal by ars on Wednesday September 13, 2017 @09:53PM (#15244432)

> necessary to represent an arbitrary natural number

What makes you think this number exists? Infinities can not be added and divided this way.

> The average can't be larger than the largest number.

But it can be equal to it. You mistake is not realizing that infinity minus 1 = infinity.

So the average is "smaller" than the largest, and yet equal to it. Because like I said at the start, you can not just add infinities in the normal way you can manipulate finite numbers.

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