Integers are numbers that can be written without a fractional component. For example, 10, 42 or -8987 are integers while 1.5 or *π* not.

Integers contains natural numbers, zero and negative counterpart for each natural number. Usually we denote integers as *ℤ*, from the german word “Zahl” which means “number” in english. We can write that the set of integers is equal to

ℤ = { − 3, − 2, − 1, 0, 1, 2, 3}.

## Properties of Integers

- Since integers contains the set of natural numbers, the set of all integers is infinite set.
- Integers are closed under addition. It means that if you add any two integers you will always get another integer. Try it! E. g.
*5 + 6 = 11*or*− 6 + 2 = − 4*. All of them are integers. - The same goes for multiplication. We can multiply any two integers and we always get another integer. E. g.
*2 · 7 = 14*or*− 3 · 0 = 0*. - The same goes for subtraction. E. g.
*7 − 10 = − 3*, all of them integers. This differs from the natural numbers. - Integers are not closed under division. For example,
*5 / 2 = 2.5*and 2.5 is not integer.

## Graphical Representation of Integers

We can show integers using a simple graph with a single axis:

There are infinite amount of integers, we just highlighted 11 of them.