Yes. They just can't have fractional parts.
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The product of two integers will be: * Zero, if one factor, or both, are zero. * Positive, if both factors have the same sign (both positive, or both negative) * Negative, if the two factors have different signs. Actually, these rules apply to all real numbers, not just to integers.
Negative integers, zero and the positive integers, together form the set of integers.
Yes, the intersection of non-negative (positive) and non-positive (negative) integers is zero.
positive integers
They are called integers. Fractions and decimals are NOT integers, even if it has a positive or negative sign.