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Single Idea 18465

[filed under theme 8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation ]

Full Idea

R is an equivalence relation on A iff R is reflexive, symmetric and transitive on A.

Gist of Idea

An 'equivalence' relation is one which is reflexive, symmetric and transitive

Source

Kenneth Kunen (The Foundations of Mathematics (2nd ed) [2012], I.7.1)

Book Ref

Kunen,Kenneth: 'The Foundations of Mathematics' [College Publications 2012], p.24

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The 2 ideas with the same theme [a transitive, symmetrical, reflexive relation]:

10585

Symmetrical and transitive relations are formally like equality [Russell]

18465

An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen]