Question

Are integers always, sometimes, or never whole numbers?

Answer 1

Integers are always whole numbers, positive, negative or 0.

Explanation:

Rational numbers are those which can be written in the form of `a/b, b!=0`

Within the rational numbers there are two groups

• fractions such as `12/3` which simplify to whole numbers and
• fractions which do not give whole numbers. (`3/4, 1.7, -9/5`)

The whole number group are called Integers `(ZZ )`which can be positive, negative or zero.

Integers are divided into two groups

• the negative integers (-1, -2, -3, .....) and
• counting numbers (0, 1,2,3,4...)

Answer 2

`color(brown)("So if an integer is the sum or difference of whole numbers")` `color(brown)("then an integer is always a whole number.")`

Explanation:

From Collins Dictionary of Mathematics:

`"integer"`, n, also called 'signed number' or 'directed number'. a number that may be expressed as the sum or difference of 2 natural numbers; a member of the set {...-3, -2, -1, 0, 1, 2, 3...} usually denoted as `ZZ`.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("So if an integer is the sum or difference of whole numbers")` `color(brown)("then an integer is always a whole number.")`