equivalence relation

A binary relation R on a set A is an equivalence relation if it is also a

There are multiple ways that equivalence relations are notated, but the most common are “a ~ b” and “a ≡ b” when it is obvious that a relation R is being referenced. Otherwise the equivalence may be denoted “a ~Rb“, “a ≡Rb“, or “aRb“.

So for every a, b, c in set A and

  • a ~ a (Reflexivity)
  • if a ~ b if and only if b ~ a (Symmetry) 
  • if a ~ b and b ~ c, then a ~ c (Transitivity)

 

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