Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Equivalence classes

  1. Jun 1, 2012 #1
    Given the set S, where aSb if and only if a - b [itex]\in[/itex] [itex]Z[/itex]

    It is asking for the equivalence class and the answer given is
    S has only one equivalance class for each real number x such that 0 ≤ x < 1. the class [x] is given by {x + k : k [itex]\in[/itex] [itex]Z[/itex]}

    i dun get it, since S is a set of relation where a - b is an element of Z, then there should be a lot of equivalance class for S, however, it states that S has only one equivalence class and its {x + k}
     
  2. jcsd
  3. Jun 1, 2012 #2

    chiro

    User Avatar
    Science Advisor

    Hey look416.

    The equivalence class seems to be defined in terms of the usual way (in terms of a modulus like definition) and since you are dealing with integers this seems appropriate (the final thing is going to be a set of integers).
     
  4. Jun 1, 2012 #3
    but its stating it owns one equivalence class only, i thought there should be infinite sets of classes?
     
  5. Jun 1, 2012 #4

    Stephen Tashi

    User Avatar
    Science Advisor


    The answer said "one equivalence class for each real number....etc. ", not "one equivalence class".
     
  6. Jun 1, 2012 #5
    ok,but that raise me to another problem
    it says that for each real number x such that 0 ≤ x < 1. , which means that the whole relation only valids for that range?
    requires some help on understanding the relation between the a-b and x
     
  7. Jun 1, 2012 #6

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Well, there is an equivalence class for 1.5 too (for example), but that is equal to the equivalence class of 0.5 (since 1.5-0.5 is in Z). So every equivalence class can be written as [itex]\{x+k~\vert~k\in \mathbb{Z}\}[/itex] with x in [0,1[.
     
  8. Jun 1, 2012 #7
    oh, so the variable x is account for the decimals among the integers, i see
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Equivalence classes
  1. Equivalence Class (Replies: 0)

  2. Equivalence class help (Replies: 2)

Loading...