Integers are the set of numbers {…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …} that encompass the counting numbers, {1, 2, 3, …}, the negative of the counting numbers, {… -3, -2, -1} and zero. Integers can be shown on a simple number line.

The integers on the left side of zero (0) are called negative numbers, and are represented by a negative sign (-) placed before them, as in -5, -10, and -15.* The integers on the right side of 0 are called positive numbers. Examples include 5, 10, and 15. The positive integers are known as counting numbers or natural numbers. The positive integers and 0 are called whole numbers. Zero is an integer but it is neither positive nor negative.

*Some historians believe the first evidence of the use of negative numbers was around 300 B.C.E. in China.

Integers are used in everyday life. A debt or a loss is often expressed with a negative integer. A gain is usually expressed with a positive integer. When the temperature is warmer than the zero point of the temperature scale, it is represented with a positive sign; when it is colder than the zero point, it is represented with a negative sign.

See Also

Numbers, Real; Numbers, Whole; Zero.

Bibliography

Aufmann, Richard N., and Vernon C. Baker. Basic College Mathematics, 4th ed. Boston: Houghton Mifflin Company, 1991.