Single Idea 8920

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

Full Idea

A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'.

Gist of Idea

Equivalence relations are reflexive, symmetric and transitive, and classify similar objects


Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9)

Book Reference

Lipschutz,Seymour: 'Set Theory and related topics (2nd ed)' [McGraw-Hill 1998], p.73

A Reaction

So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part