1

The number one (1) 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. The number 1 is sometimes also called ``unity,'' so the $n$th roots of 1 are often called the $n$th 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

$${1\over 1-x}=1+x+x^2+x^3+x^4+\ldots.$$

See also 2, 3, Exactly One, Root of Unity, Unique, Unit Fraction, Zero