Single Idea 10085

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

Full Idea

The set of ordered pairs of natural numbers (i,j) is effectively enumerable, as proven by listing them in an array (across: <0,0>, <0,1>, <0,2> ..., and down: <0,0>, <1,0>, <2,0>...), and then zig-zagging.

Gist of Idea

The set of ordered pairs of natural numbers <i,j> is effectively enumerable

Source

Peter Smith (Intro to Gödel's Theorems [2007], 02.5)

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.16