Equivalance Class

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Definition

Let be an Equivalence Relation on the set . For a given we call the equivalence class of .

Representatives

An element is called a representative of with

Theorem

1. - this follows by definition of Equivalence Relation
2. If then or .

Examples

1. Let and if is divisible by 2 (i.e. the difference is an even number):

   • 𝕫

2. Let and if , i.e.

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Appendix

• Tags:
  • Math, Set Theory
• Reference:
  • + 03 Äquivalenzklassen
• Related: