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Equivalence class help

  1. Mar 21, 2012 #1
    Why in equivalence class of N of even number and odd number, the even number are taken as related to 0 and odd number are related as 1 i.e [0] and [1].

    Instead of [0], even number can also be related to [2] or [4]??? Or [2] or [4] could also be taken, as it is just an convention.

    Thanks.
     
  2. jcsd
  3. Mar 21, 2012 #2
    Yes, any even number can be taken as a "representative" of its equivalence class. The important thing is that addition of equivalence classes doesn't depend on the choice of representative, i.e.
    [even]+[even]=[even], [odd]+[even]=[even]+[odd]=[odd], [odd]+[odd]=[even].
     
  4. Mar 21, 2012 #3
    thanks a lot!!!
     
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