more from Richard Dedekind

### Single Idea 10183

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets]

Full Idea

A set is 'Dedekind-infinite' iff there exists a one-to-one function that maps a set into a proper subset of itself.

Gist of Idea

An infinite set maps into its own proper subset

Source

report of Richard Dedekind (Nature and Meaning of Numbers [1888], §64) by E Reck / M Price - Structures and Structuralism in Phil of Maths n 7

A Reaction

Sounds as if it is only infinite if it is contradictory, or doesn't know how big it is!