Hume's principle

Statement

In the foundations of mathematics, Hume's principle (or HP) says that, given two collections of objects $\mathcal F$ and $\mathcal G$ with properties $F$ and $G$ respectively, the number of objects with property $F$ is equal to the number of objects with property $G$ if and only if there is a one-to-one correspondence (a bijection) between $\mathcal F$ and $\mathcal G$. In other words, that bijections are the "correct" way of measuring size.