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you showed it was an equivalence relation right?

so what, for example, is in the equivalence class of \(2\)?

So wouldn't the equivalence class for 2 be -2 and +2?

yes

so for any integer n, it'd be, -n and +n?

in fact all equivalence classes have to elements, except 0 which is in its own class

what would be the correct notation to write that all?

idk depends on how you write them

\[\{a,-a\}\] maybe

and a = N?

i do no like your proof however, you have the if and then in the wrong place

oo! kk, i'll go back and edit that. How should i make it better?