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What Is an Integer? (Mathematics Lesson)

What Is an Integer?

An integer is a whole number.

The integers are:



Integers may be positive, negative, or zero.

Mathematicians use the symbol to represent the set of integers.

Ordering of Integers

Integers can be represented on a number line:



The arrows at each end of the line indicate that the numbers go on forever in each direction.

The further right on the number line an integer is, the greater it is:

  • any integer is greater than any integer to its left.
  • any integer is less than any integer to its right.
This means that 3 is greater than 2, but -3 is less than -2.

Properties of Integers

The slider below shows some of the properties of integers:

Quick Test
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Note
WHAT'S IN A NAME?

The word integer comes from the Latin word 'integer', meaning "whole".

The Latin word 'integer' itself is derived from the Latin 'in' ("not") + 'tangere' ("to touch").

If a number was untouched, it was unbroken, whole and entire.

This should be contrasted with the Latin root for fraction, 'fractus' meaning "broken".

WHAT DOES THE SYMBOL FOR INTEGERS MEAN?

Mathematicians use the symbol to represent the set of integers.

This symbol is a Z, from the German word 'Zahlen', meaning "numbers".