The number one (1), also called "unity," is the first positive integer. It is an odd number. Although the number 1 used to be considered a prime number, it requires special treatment in so many definitions and applications involving primes greater than or equal to 2 that it is usually placed into a class of its own (Wells 1986, p. 31). The number 1 is sometimes also called "unity," so the nth roots of 1 are often called the nth roots of unity. Fractions having 1 as a numerator are called unit fractions. If only one root, solution, etc., exists to a given problem, the solution is called unique.

The generating function having all coefficients 1 is given by


The number one is also equivalent to the repeating decimal


See also

2, 3, Complexity, Fallacy, Exactly One, Monad, One-Form, One-Mouth Theorem, One-Ninth Constant, One-Sheeted Hyperboloid, One-to-One, One-Way Function, Root of Unity, Unique, Unit Fraction, Zero

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Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, pp. 30-32, 1986.

Cite this as:

Weisstein, Eric W. "1." From MathWorld--A Wolfram Web Resource.

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