Full Idea
A 'bijective' function has 'one-to-one correspondence' - it is both surjective and injective, so that every element in each of the original and the output sets has a matching element in the other.
Gist of Idea
A 'bijective' function has one-to-one correspondence in both directions
Source
Peter Smith (Intro to Gödel's Theorems [2007], 02.1)
Book Reference
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.8
A Reaction
Note that 'injective' is also one-to-one, but only in the one direction.
Related Idea
Idea 13537 An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS]