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 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.