Is a negative number an integer?

Answer 1

Integers are all of the real numbers that can be written without using a decimal or a fraction; i.e, they're the set of all positive and negative whole numbers plus zero.

Integers have the following properties:

i) 0 exists, and is the additive identity element; 0 + a = a for all a.

ii) 1 exists, and is the multiplicative identity element; 1a = a for all a.

iii) Addition and multiplication are both associative and commutative.

iv) An additive inverse exists for all elements a, denoted as -a.

v) Distributivity.

vi) Adding or multiplying two integers yields another integer.

From iv), we know that for each a > 0, there exists an additive inverse, -a, which must be less than 0, hence a negative number.

So, there are integers that are negative numbers.

But, not every negative number is an integer. There are negative numbers that must be expressed as a decimal or a fraction. For example, -0.5 isn't an integer, because, were you to not write it as a decimal, you would have to write it as a fraction: -1/2