Define the relation R on the real numbers R by xRy if and only if x - y belong to Z, that is, x - y is an integer.

a) Describe the Partition.

(c) Prove that for every x E R there exists a y E [0; 1) such that x Ey/R.

(note:For any real number a and nonzero real

number b, there exists an integer q and a real number r such that a = qb+r and 0 <= r < lbl.)

I am having a hard time with partition, i don't know how to describe them explicitly