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
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.