Integers
The set of integers consists of the positive integers, corresponding to the natural numbers, their additive inverses, that is, the negative integers, and 0
The set of integers, denoted by ℤ (from the German Zahlen, “numbers”), is the set consisting of:
Sign, absolute value, and additive inverse
Unlike natural numbers, which have no sign, integers are preceded by a positive (+) or negative (−) sign. The only integer with no sign, and therefore neither positive nor negative, is 0.
Besides the sign, another distinctive element of integers is the absolute value, which is indicated by enclosing a number between two vertical bars (e.g., |−9|). The absolute value is the number itself considered without its sign. It represents the distance of an integer from 0 on a number line. For example, +5 and −5 are opposite to 0, but at the same distance, which is why they have the same absolute value:
Integers with equal absolute value but different signs, such as +5 and −5, are called additive inverses or opposites. Summed, they add up to 0. For…
