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Math Help - equivalence classes

  1. #1
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    equivalence classes

    I'm having trouble proving the distributive law for [r] [s] [t] in Zn (the integers mod n)

    i.e. [r]([s] + [t]) = [r][s] + [r][t]

    I did this so far.
    (r+m1*n)[(s+m2*n)+(t+m3*n)] = (r+m1*n)(s+m2*n)+(r+m3*n)(t+m4*n)
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  2. #2
    Moo
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    Hello,

    (r+m1*n)[(s+m2*n)+(t+m3*n)]= (r+m1*n)(s+m2*n)+(r+m1*n)(t+m3*n)
    *modification in red*

    Now, huum... you can see, if you develop again, you have [r][s]+[r][t]
    Last edited by Moo; September 11th 2008 at 10:17 PM.
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  3. #3
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    [r] = r+mn, the m could be different for each [r], so the first [r] could have a different m than the second.
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  4. #4
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    Here is an example how you prove it is well-defined.
    Say you wanted to prove [a]+[b]=[a+b].

    Say [a]=[c] and [b]=[d].
    This means a\equiv c ~ (n) and b\equiv d ~ (n).
    Thus, a+b\equiv c+d ~ (n) so [a+c]=[b+d].
    This shows that + is well-defined.

    Modify this argument to the problem you have.
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