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### Single Idea 10618

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

Full Idea

All numbers are related to zero by the ancestral of the successor relation.

Clarification

See Idea 10617 for the 'ancestral' relation

Gist of Idea

All numbers are related to zero by the ancestral of the successor relation

Source

Peter Smith (Intro to Gödel's Theorems [2007], 23.5)

Book Reference

Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.211

A Reaction

The successor relation only ties a number to the previous one, not to the whole series. Ancestrals are a higher level of abstraction.

Related Idea

Idea 10617
The 'ancestral' of a relation is a new relation which creates a long chain of the original relation **[Smith,P]**