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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 Ref
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]