SOLUTION: Let n∈N. Since ≡n is an equivalence relation on Z. The set of ≡n equivalence classes forms a partition of Z. How many sets are in this partition? Please explain. I don'

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Question 1196020: Let n∈N. Since ≡n is an equivalence relation on Z. The set of ≡n equivalence classes forms a partition of Z. How many sets are in this partition?
Please explain. I don't understand how to calculate how many sets are in a partition.
I think it could be n ?
Thank you.
Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
.

One set is all numbers n∈N that are multiple of n (give the remainder 0 when divided by n).

Second set is all numbers n∈N that give the remainder 1 when divided by n.

Third set is all numbers n∈N that give the remainder 2 when divided by n.

Fourth set is all numbers n∈N that give the remainder 3 when divided by n.

. . . And so on . . .

Last set is all numbers n∈N that give the remainder (n-1) when divided by n.


In all, there are n such sets in this partition.