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### Single Idea 10608

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers]

Full Idea

The number of Fs is the 'successor' of the number of Gs if there is an object which is an F, and the remaining things that are F but not identical to the object are equinumerous with the Gs.

Gist of Idea

The number of Fs is the 'successor' of the Gs if there is a single F that isn't G

Source

Peter Smith (Intro to Gödel's Theorems [2007], 14.1)

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.120