Let \(V\) be a set and let \(R\subseteq V\times V\) be a relation \(R\) is called an equivalence relation, if it is reflexive, symmetric and transitive. Elements of $V$ with $aRb$ are called equivalent. Other common notations are \(a\sim_R b\) or \(a\sim b\), if $R$ is known from the context.
Definitions: 1 2 3 4 5
Examples: 6
Explanations: 7
Lemmas: 8
Motivations: 9
Parts: 10 11
Proofs: 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Propositions: 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
Solutions: 44
Theorems: 45