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Thread: equivalence classes

  1. #1
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    equivalence classes

    Give the representative between 0 and 9 of the equivalence class in
    Z10 that the number
    -3 + 2 x 10 + 3 x10^2 + 20 - 1x 5 is a member of.
    So do I make the values in the set {0,1,2,3,4,5,6,7,8,9 } and assign the equation ?
    I'm not too sure how to do this any help would be appreciated thanks.
    You must be very careful on your use on mathematical language.
    To say that x is a number between 0 & 9 means $0<x<9$.
    To say that x is a number from 0 to 9 means $0\le x\le 9$.

    Which of those do you mean here?
    Last edited by bee77; Sep 11th 2017 at 06:36 PM.
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    Re: equivalence classes

    Oh it's Between
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  3. #3
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    Re: equivalence classes

    Oh it's Between 0<x<9
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  4. #4
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    Re: equivalence classes

    First, do the given calculation: -3 + 2 x 10 + 3 x10^2 + 20 - 1x 5= -3+ 20+ 300+ 20- 5= 340- 8= 332. Now Z_{10} is the set of integer modulo 10: what is the remainder when 332 is divided by 10? Without doing any arithmetic at all you should be able to see it is 2.

    (Oh, Z_{10} is not "Between 0< x< 0", it is in 0\le x\le 9.)
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  5. #5
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    Re: equivalence classes

    Thanks HallsofIvy been pretty busy sorry for late reply ,mid semester is getting bombarded with 500 things at once ..sigh
    cheers
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