Thread: help understanding an equivalence relation

I'm having trouble understanding what the professor ment when he wrote/explained this:

A= integers, xRy iff 4|(x-y)

[0]={yE integers: yR0}
={yE integers: 4|0}
={multiples of 4+1}

note: -that yE integers means y is an element of integers
-iff means if and only if
-| means divides
-yR0 means y is in relation to 0 (or so i read it)

-why are we saying that yE integers instead of saying that x,yE integers? are we trying to show reflexivity in this case?

-why does 4|0? if we were to use the equivalence relation [1] or [2], would it then be 4|[1] or 4|[2]?

any brief explanation would be great =)

i've discovered the answer, but not enough to answer my new posted thread.

sorry for the inconvenience