How To Find An Integer

What is an integer and what are examples of integers?

An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or nil.

Examples of integers are: -five, 1, 5, 8, 97, and 3,043.

Examples of numbers that are not integers are: -ane.43, 1 three/4, 3.xiv, .09, and 5,643.1.

The set of integers, denoted Z , is formally defined as follows:

Z = {..., -3, -2, -i, 0, 1, two, 3, ...}

In mathematical equations, unknown or unspecified integers are represented by lowercase, italicized messages from the "late centre" of the alphabet. The nigh common are p, q, r, and due south.

The set Z is a denumerable set. Denumerability refers to the fact that, even though there might exist an space number of elements in a ready, those elements can be denoted past a list that implies the identity of every element in the set. For example, it is intuitive from the listing {..., -3, -ii, -ane, 0, one, 2, 3, ...} that 356,804,251 and -67,332 are integers, simply 356,804,251.5, -67,332.89, -four/3, and 0.232323 ... are non.

The elements of Z can be paired off one-to-one with the elements of N , the prepare of natural numbers, with no elements being left out of either fix. Let North = {1, 2, 3, ...}. Then the pairing can continue in this manner:

integer.gif (1078 bytes)

In infinite sets, the existence of a one-to-ane correspondence is the litmus examination for determining cardinality, or size. The gear up of natural numbers and the prepare of rational numbers have the same cardinality as Z . However, the sets of real numbers, imaginary numbers, and complex numbers have cardinality larger than that of Z .

This was last updated in Oct 2021

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