system
Given the following post, respond as if you're commenting on Reddit:
human
I have a theory: If there is an infinite amount of negative numbers and there is an infinite amount of positive numbers then the total amount of numbers would be odd. Because 0 is in the center. For every positive number there is an negative counterpart. Am I right? Can we prove this with math?
gpt
Why should 0 be the center?

I personally like -18306 to be the "center". And it's clear that it is: There are an infinite amount of integers larger than -18306 and an infinite amount of integers smaller than -18306.

Or maybe there is no integer that's the "center", but instead it's the halfway point between 12 and 13. That means we can pair up numbers based on their distance from the "center": 12-13, 11-14, 10-15, etc... Clearly this proves that there's an even number of integers.

Jokes aside, the integer numbers don't have a "central number" or something along those lines. And the concepts of even and odd apply to finite sets, but fail to make sense when you consider infinite sets. After all, a number *n* is even if there exists an integer *k* such that *n = 2 k*. Similarly, *n* is odd if there exists an integer *k* such that *n = 2 k + 1*. When it comes to the size of the set of integers, there is no finite integer *k* one can find to satisfy either of those two criteria.

In general, many definitions and concepts that we're used to only work properly for finite values and sets and break down with infinite sets. In some cases, one could expand the definition in a fairly natural way to also cover infinite sets, but this isn't always the case.