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!