This article is about the number. For the year, see AD 1. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number 1st valentine gift for husband by 1 equals the same number. Most if not all properties of 1 can be deduced from this.

In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. The unique mathematical properties of the number have led to its unique uses in other fields, ranging from science to sports. It commonly denotes the first, leading, or top thing in a group. The word one can be used as a noun, an adjective, and a pronoun.

One, sometimes referred to as unity, is the first non-zero natural number. It is thus the integer after zero. Any number multiplied by one remains that number, as one is the identity for multiplication. 24-hour clock face, one through twelve clockwise on right, and one through twelve again clockwise on left, with J shapes where ones’ digits would be expected when numbering the clock hours. Shadow suggests 3 PM toward the lower left.

This Woodstock typewriter from the 1940s lacks a separate key for the numeral 1. Hoefler Text, a typeface designed in 1991, represents the numeral 1 as similar to a small-caps I. The glyph used today in the Western world to represent the number 1, a vertical line, often with a serif at the top and sometimes a short horizontal line at the bottom, traces its roots back to the Brahmic script of ancient India, where it was a simple vertical line. In some countries, the serif at the top is sometimes extended into a long upstroke, sometimes as long as the vertical line, which can lead to confusion with the glyph used for seven in other countries. In styles in which the digit 1 is written with a long upstroke, the digit 7 is often written with a horizontal stroke through the vertical line, to disambiguate them.

Many older typewriters lack a separate key for 1, using the lowercase letter l or uppercase I instead. It is possible to find cases when the uppercase J is used, though it may be for decorative purposes. In some typefaces, different glyphs are used for I and 1, but the numeral 1 resembles a small caps version of I, with parallel serifs at top and bottom, with the capital I being full-height. Formalizations of the natural numbers have their own representations of 1. In the Peano axioms, 1 is the successor of 0. However, 1 is especially common for the multiplicative identity of a ring, i.

By definition, 1 is the probability of an event that is absolutely or almost certain to occur. In category theory, 1 is sometimes used to denote the terminal object of a category. This is more formally referred to as a unary numeral system. There are two ways to write the real number 1 as a recurring decimal: as 1.

In many mathematical and engineering problems, numeric values are typically normalized to fall within the unit interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters. The definition of a field requires that 1 must not be equal to 0. Thus, there are no fields of characteristic 1. Nevertheless, abstract algebra can consider the field with one element, which is not a singleton and is not a set at all. 1 is the most common leading digit in many sets of data, a consequence of Benford’s law. 1 is the only known Tamagawa number for a simply connected algebraic group over a number field.