more from A.George / D.J.Velleman

Single Idea 10104

[catalogued under 4. Formal Logic / F. Set Theory ST / 3. Types of Set / e. Equivalence classes]

Full Idea

A relation is an equivalence relation if it is reflexive, symmetric and transitive. The 'same first letter' is an equivalence relation on the set of English words. Any relation that puts a partition into clusters will be equivalence - and vice versa.

Gist of Idea

'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words


A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.64

A Reaction

This is a key concept in the Fregean strategy for defining numbers.