1. ## 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?

2. ## Re: equivalence classes

Oh it's Between

3. ## Re: equivalence classes

Oh it's Between 0<x<9

4. ## 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 $0\le x\le 9$.)

5. ## Re: equivalence classes

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