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