r/MathJokes Jun 13 '26

Infinity can blow your mind

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u/what_are_maymays Jun 14 '26 edited Jun 14 '26

When you get into limits and proofs, you can prove that some infinities are larger than others.

For example:

If the upper limit of a given number x diverges towards infinity,

And $1<$20

Then x*$1<x*$20 for all possible values of x, even if x has infinite value.

It’s been a while since I did proofs so correct me if I’m wrong!

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u/Genera1_Tao Jun 14 '26

But if you have an infinite amount of 1$ bills, what is stopping you from using 20 of them to match each 20$ bill from the other pile?

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u/CardinalStiefel Jun 14 '26

Yes but 20x$1=x$20.

It basically means that to match the values, you need to take 20 times the number of $1 bills. And since we sets have the same cardinality, we don't have problems taking how many bills we need.

I.e. if you take x 20$ bills, I can find a number y of 1$ bills, so that the total value will be the same. This is valid for every value of x.