Question

why integers are represented by z?

Answer 1

INTEGERS ARE DENOTED BY Z BECAUSE IT HAS AN ANOTHER NAME ZAHLEN,SO IT IS DENOTED BY Z

Answer 2

It was started by N. Bourbaki.
He denoted the integers with z so we are following that!
And he used it because z stands for Zahlen ( a German word) which means numbers.
Hope this helps!!