more from Peter Smith

### Single Idea 10079

#### [catalogued under 5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms]

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]**