numbers

A concept used initially in counting, to compare the sizes of groups of objects. Natural numbers (or cardinal numbers) are the numbers used in counting, 1,2,3,4,5.... These are always whole numbers. The set of integers comprises all the natural numbers (the positive integers), zero, and the negative numbers...?3,?2,?1. The rational numbers are all the numbers that can be expressed in the form m/n, where m and n are two integers, positive or negative. Rational numbers include proper fractions (those whose numerator is less than their denominator, eg ?) and improper fractions (those whose numerator is greater than their denominator, eg ?). Mixed numbers are the sum of an integer and a proper fraction, eg 2½. Decimal fractions are those with denominator a power of 10, written as 0·3, 0·345, etc. Recurring decimals are decimal fractions where a sequence of digits is repeated, eg 0·037037037..., which can be written 0·?3?, and is equal to ?, or ?. All recurring decimals can be expressed as rational numbers.

Irrational numbers are all real numbers that are not rational. Some can be expressed as the roots of algebraic equations with rational coefficients, eg ?3 is a root of x² = 3. Those that cannot be so expressed are called transcendental numbers, eg ?, e, e². Real numbers are all numbers that do not contain an imaginary number (a square root of a negative number). The positive square root of ?1 is denoted by i (occasionally j). Complex numbers have a real and an imaginary part, eg 3 + 4i. Either part of a complex number can be zero, so that all real numbers can be considered to be complex. The majority of real numbers are transcendental - a surprising proposition, but true, for ?, ?², ?³..., etc are all transcendental numbers. To any non-transcendental number, say k, there correspond an infinite number of transcendentals, such as k + ?, k + ?², k + ?³,....

The word number can also refer to

Telephone numbers. Grammatical number, a morphological grammatical category indicating the quantity of referents Number (music), a self-contained piece of music that is combined with other such pieces in a performance The "Book of Numbers", part of the Torah, the fourth book of the Bible. A Numbers game, a gambling scheme common in poor US urban neighborhoods. NUMB3RS, an American TV show on CBS The Numbers in Lost (TV series): 4, 8, 15, 16, 23 and 42 "Numbers (Lost)," a focal episode of Season 1 in the series Numbers (Cat Stevens album) (subtitled "A Pythagorean Theory Tale"), an album by Cat Stevens Number (game), a number-guessing computer game. If an internal link led you here, you may wish to change the link to point directly to the intended article.