If a set has $n$ elements then what are maximum number of equivalence classes and equivalence relations possible on it?
[Math] Number of equivalence relations on a set
algebra-precalculuscombinatoricsdiscrete mathematicselementary-set-theory
algebra-precalculuscombinatoricsdiscrete mathematicselementary-set-theory
If a set has $n$ elements then what are maximum number of equivalence classes and equivalence relations possible on it?
Best Answer
The maximum number of equivalence classes is $n$ -the identity relation $\{ (x,x) \ | \ x \in X \}$ is an equivalence relation. The number of equivalence relations is the Bell number. The series is in A000110 of OEIS.