Mathematical
Galileo's Paradox
There are as many perfect squares as there are natural numbers
Overview
An early observation about infinity showing that infinite sets can be placed in one-to-one correspondence with proper subsets of themselves.
Every natural number can be paired with its square: 1↔1, 2↔4, 3↔9, etc. So there are as many squares as natural numbers. But squares are a subset of natural numbers, so there should be fewer. Which is it?