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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
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.3)
Book Ref
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.
9854 | We can introduce new objects, as equivalence classes of objects already known [Frege, by Dummett] |
9883 | Frege introduced the standard device, of defining logical objects with equivalence classes [Frege, by Dummett] |
9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
8920 | Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz] |
10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |