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Homework Help: Identifying equivalence classes with the unit circle

  1. Oct 16, 2011 #1
    1. The problem statement, all variables and given/known data

    Define a relation on R as follows. For a,b ∈ R, a ∼ b if a−b ∈ Z. Prove that this is an equivalence relation. Can you identify the set of equivalence classes with the unit circle in a natural way?

    2. Relevant equations

    3. The attempt at a solution

    I have already proven that this is an equivalence relation but i do not understand how the equivalence classes relate to the unit circle
    Last edited: Oct 16, 2011
  2. jcsd
  3. Oct 16, 2011 #2


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    One fairly obvious equivalence relation on the unit circle can be obtained by considering the results of using θ and (2π + θ) as arguments of the trig functions.
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