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### Single Idea 10081

#### [catalogued under 5. Theory of Logic / K. Features of Logics / 8. Enumerability]

Full Idea

A set is 'enumerable' iff either the set is empty, or there is a surjective function to the set from the set of natural numbers, so that the set is in the range of that function.

Clarification

For 'surjective' see Idea 10077

Gist of Idea

A set is 'enumerable' is all of its elements can result from a natural number function

Source

Peter Smith (Intro to Gödel's Theorems [2007], 02.3)

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.13

Related Idea

Idea 10077
A 'surjective' ('onto') function creates every element of the output set **[Smith,P]**