Cosets as equivalence classes ↩

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created: 2021-12-06 14:06:49
modified: 2022-01-10 04:13:02

Since we know that every element of a coset, represents the coset fully in the sense that , it is easy to prove that for a group and any :

  1. Being in the same left closet of is an equivalence relation on
  2. With the equivalence classes being the cosets themselves