Integer

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 , 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:

Integers on x-axis

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