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Question about cosets

  1. Nov 19, 2004 #1
    so let H = { 0, 3, 6} under Z(9), and I need to find a + H.

    the book shows

    0 + H = 3 + H = 6 + H
    1 + H = 4 + H = 7 + H
    2 + H = 5 + H = 8 + H.

    I"m not understanding why they start with 0, 1, 2. what gives that away?
     
  2. jcsd
  3. Nov 19, 2004 #2

    matt grime

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    They find the coset of each element in the nice logical order that comes from the fact that 0<1<2, and that completely enumerates all the cosets. You've got to start somewhere, why not there?
     
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