In the Peano axioms, 1 is the successor of 0. more generally, in algebra, the multiplicative identity (also called unity), usually of a group or a ring.įormalizations of the natural numbers have their own representations of 1.in arithmetic ( algebra) and calculus, the natural number that follows 0 and the multiplicative identity element of the integers, real numbers and complex numbers.Hoefler Text, a typeface designed in 1991, represents the numeral 1 as similar to a small-caps I. While the shape of the character for the digit 1 has an ascender in most modern typefaces, in typefaces with text figures, the glyph usually is of x-height, as, for example, in. Styles that do not use the long upstroke on digit 1 usually do not use the horizontal stroke through the vertical of the digit 7 either. 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. 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. It was transmitted to Europe via the Maghreb and Andalusia during the Middle Ages, through scholarly works written in Arabic. 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. Main article: History of the Hindu–Arabic numeral system It is also the only natural number that is neither composite nor prime with respect to division, but is instead considered a unit (meaning of ring theory). One is also the result of the empty product, as any number multiplied by one is itself. As a result, 1 is its own factorial, its own square and square root, its own cube and cube root, and so on. It is thus the integer after zero.Īny number multiplied by one remains that number, as one is the identity for multiplication. One, sometimes referred to as unity, is the first non-zero natural number. Ĭompare the Proto-Germanic root *ainaz to Old Frisian an, Gothic ains, Danish en, Dutch een, German eins and Old Norse einn.Ĭompare the Proto-Indo-European root *oi-no- (which means "one, single" ) to Greek oinos (which means "ace" on dice ), Latin unus (one ), Old Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin and Breton un (one ). The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no. It comes from the English word an, which comes from the Proto-Germanic root *ainaz. The word one can be used as a noun, an adjective, and a pronoun. It commonly denotes the first, leading or top thing in a group. The unique mathematical properties of the number have led to its unique uses in other fields, ranging from science to sports. 1 is by convention not considered a prime number although universally accepted today, this fact was controversial until the mid-20th century. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. Most if not all properties of 1 can be deduced from this. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. For example, a line segment of unit length is a line segment of length 1. It represents a single entity, the unit of counting or measurement. 1 ( one, also called unit, and unity) is a number and a numerical digit used to represent that number in numerals.