Integers are the natural numbers, the opposites of the natural numbers, and zero.
Integers = {... -3, -2, -1, 0, 1, 2, 3, ...}
As you can see the set of integers has positive numbers as well as zero and negative numbers.
The figure below illustrates the set of integers.
Positive integers are integers that are bigger than zero. The positive integers are
{1, 2, 3, ...}
Negative integers are integers that are smaller than zero. The negative integers are
{... -3, -2, -1}
Zero is neither positive nor negative!