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Look up one in Wiktionary, the free dictionary.

1 (one) is a number, numeral, and the name of the glyph representing that number. It represents a single entity. One is sometimes referred to as unity or unit as an adjective. For example, a line segment of "unit length" is a line segment of length 1. The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. ... The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... In mathematics and computer science, hexadecimal, base-16, or simply hex, is a numeral system with a radix, or base, of 16, usually written using the symbols 0–9 and A–F, or a–f. ... Wikipedia does not have an article with this exact name. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 151 languages. ... No file by this name exists; you can upload it. ... No file by this name exists; you can upload it. ... For other uses, see Number (disambiguation). ... A numeral is a symbol or group of symbols that represents a number. ... variant glyphs representing the character a (allographs of a) in the Zapfino typeface. ... The geometric definition of a line segment In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. ... For other uses of this word, see Length (disambiguation). ...

In mathematics, it may represent:

• historically, the first ordinal number, though some modern conventions use 0 (number) as the first ordinal
• the natural number following 0 and preceding 2, the multiplicative identity of the integers
• the corresponding real number 1, the multiplicative identity of the real and complex numbers
• in abstract algebra, it is the multiplicative identity

In set theory, ordinal, ordinal number, and transfinite ordinal number refer to a type of number introduced by Georg Cantor in 1897, to accommodate infinite sequences and to classify sets with certain kinds of order structures on them. ... Zero redirects here. ... In mathematics, a natural number can mean either an element of the set {1, 2, 3, ...} (i. ... Zero redirects here. ... For other uses of 2, see 2 (disambiguation). ... In mathematics, the term identity has several important uses: An identity is an equality that remains true regardless of the values of any variables that appear within it, to distinguish it from an equality which is true under more particular conditions. ... Not to be confused with Natural number. ... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram In mathematics, the complex numbers are the extension of the real numbers obtained by adjoining an imaginary unit, denoted i, which satisfies:[1] Every complex number can be... Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ...

Mathematics

For any number x:

x·1 = 1·x = x (1 is the multiplicative identity)

x/1 = x (see division)

x¹ = x, 1^x = 1, and for nonzero x, x⁰ = 1 (see exponentiation)

Using ordinary addition, we have 1 + 1 = 2. In mathematics, multiplication is an elementary arithmetic operation. ... In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ... “Exponent” redirects here. ... 3 + 2 = 5 with apples, a popular choice in textbooks[1] This article is about addition in mathematics. ... For other uses of 2, see 2 (disambiguation). ...

One cannot be used as the base of a positional numeral system; sometimes tallying is referred to as "base 1", since only one mark (the tally) is needed, but this is not a positional notation. This article is about different methods of expressing numbers with symbols. ... Tally marks are a variation of the unary numeral system. ...

The logarithms base 1 is undefined, since 1^x=1 and so has no unique inverse function.-1... A function ƒ and its inverse ƒ–1. ...

In the real number system, 1 can be represented in two ways as a recurring decimal: as 1.000... and as 0.999... (q.v.). In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... A recurring or repeating decimal is a number which when expressed as a decimal has a set of final digits which repeat an infinite number of times. ... In mathematics, the recurring decimal 0. ...

In the Von Neumann representation of natural numbers, 1 is defined as the set {0}. This set has cardinality 1 and hereditary rank 1. Sets like this with a single element are called singletons. In mathematics, the Peano axioms (or Peano postulates) are a set of second-order axioms proposed by Giuseppe Peano which determine the theory of the natural numbers. ... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ... In mathematics, the cardinality of a set is a measure of the number of elements of the set. There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers. ... In axiomatic set theory and related branches of mathematics, the Von Neumann universe, or Von Neumann hierarchy of sets is the class of all sets, divided into a transfinite hierarchy of individual sets. ... In mathematics, a singleton is a set with exactly one element. ...

In Principia Mathematica, 1 is defined as the set of all singletons. The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910-1913. ... In mathematics, a singleton is a set with exactly one element. ...

In a multiplicative group or monoid, the identity element is sometimes denoted "1", but "e" (from the German Einheit, unity) is more traditional. However, "1" is especially common for the multiplicative identity of a ring. (Note that this multiplicative identity is also often called "unity".) This picture illustrates how the hours on a clock form a group under modular addition. ... In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single, associative binary operation and an identity element. ... For other uses, see identity (disambiguation). ... In mathematics, a ring is an algebraic structure in which addition and multiplication are defined and have properties listed below. ...

One is its own factorial, and its own square and cube (and so on, as 1 × 1 × ... × 1 = 1). One is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number to name just a few. For factorial rings in mathematics, see unique factorisation domain. ... A figurate number is a number that can be represented as a regular and discrete geometric pattern (e. ... A triangular number is the sum of the n natural numbers from 1 to n. ... A visual representation of the first six pentagonal numbers A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. ... It has been suggested that this article or section be merged into Centered polygonal number. ...

Because of the multiplicative identity, if f(x) is a multiplicative function, then f(1) must equal 1. In number theory, a multiplicative function is an arithmetic function f(n) of the positive integer n with the property that f(1) = 1 and whenever a and b are coprime, then f(ab) = f(a) f(b). ...

It is also the first and second numbers in the Fibonacci sequence, and is the first number in many mathematical sequences. As a matter of convention, Sloane's early Handbook of Integer Sequences added an initial 1 to any sequence that didn't already have it, and considered these initial 1's in its lexicographic ordering. Sloane's later Encyclopedia of Integer Sequences and its Web counterpart, the On-Line Encyclopedia of Integer Sequences, ignore initial ones in their lexicographic ordering of sequences, because such initial ones often correspond to trivial cases. A tiling with squares whose sides are successive Fibonacci numbers in length In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci. ... The On-Line Encyclopedia of Integer Sequences (OEIS) is an extensive searchable database of integer sequences, freely available on the Web. ...

One is the empty product. In mathematics, an empty product, or nullary product, is the result of multiplying no numbers. ...

One is the smallest positive odd integer.

One is a harmonic divisor number. A harmonic divisor number, or Ore number, is a number whose divisors, averaged in a harmonic mean, results in an integer. ...

One is often the internal representation of the Boolean constant true in computer systems. In computer science, the Boolean datatype, sometimes called the logical datatype, is a primitive datatype having one of two values: non-zero (often 1, or -1) and zero (which are equivalent to true and false, respectively). ...

One is neither a prime number nor a composite number, but a unit, like -1 and, in the Gaussian integers, i and -i. The fundamental theorem of arithmetic guarantees unique factorization over the integers only up to units (e.g. 4 = 2² = (-1)⁴×1²³×2²). In mathematics, a prime number (or a prime) is a natural number greater than 1 which has exactly two distinct natural number divisors: 1 and itself. ... A composite number is a positive integer which has a positive divisor other than one or itself. ... In mathematics, a unit in a ring R is an element u such that there is v in R with uv = vu = 1R. That is, u is an invertible element of the multiplicative monoid of R. The units of R form a group U(R) under multiplication, the group of... A Gaussian integer is a complex number whose real and imaginary part are both integers. ... In mathematics, the imaginary unit (or sometimes the Latin or the Greek iota, see below) allows the real number system to be extended to the complex number system . ... In number theory, the fundamental theorem of arithmetic (or unique factorization theorem) states that every natural number either is itself a prime number, or can be written as a unique product of prime numbers. ... ...

One was formerly considered prime by some mathematicians, using the definition that a prime is divisible only by one and itself. However, this complicates the fundamental theorem of arithmetic, so modern definitions exclude units. The last professional mathematician to publicly label 1 a prime number was Henri Lebesgue in 1899. In mathematics, a prime number (or a prime) is a natural number greater than 1 which has exactly two distinct natural number divisors: 1 and itself. ... In number theory, the fundamental theorem of arithmetic (or unique factorization theorem) states that every natural number either is itself a prime number, or can be written as a unique product of prime numbers. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Henri Lebesgue Henri Léon Lebesgue (June 28, 1875, Beauvais – July 26, 1941, Paris) was a French mathematician, most famous for his theory of integration. ...

One is one of three possible values of the Möbius function: it takes the value one for square-free integers with an even number of distinct prime factors. The classical Möbius function is an important multiplicative function in number theory and combinatorics. ... In mathematics, a square-free, or quadratfrei, integer is one divisible by no perfect square, except 1. ...

One is the only odd number in the range of Euler's totient function φ(x), in the cases x = 1 and x = 2. The first thousand values of φ(n) In number theory, the totient (n) of a positive integer n is defined to be the number of positive integers less than or equal to n and coprime to n. ...

One is the only 1-perfect number (see multiply perfect number). In mathematics, a multiply perfect number (also called multiperfect number or pluperfect number) is a generalization of a perfect number. ...

By definition, 1 is the magnitude or absolute value of a unit vector and a unit matrix (more usually called an identity matrix). Note that the term unit matrix is usually used to mean something quite different. The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs. ... In mathematics, the absolute value (or modulus[1]) of a real number is its numerical value without regard to its sign. ... In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length, (or magnitude) is 1. ... In linear algebra, the identity matrix of size n is the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. ... In linear algebra, the identity matrix of size n is the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. ...

One is the most common leading digit in many sets of data, a consequence of Benford's law. A logarithmic scale bar. ...

List of basic calculations

Multiplication	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20		21	22	23	24	25		50	100	1000
	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20		21	22	23	24	25		50	100	1000

Division	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15
	1	0.5		0.25	0.2			0.125		0.1
	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15

Exponentiation	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20
	1	1	1	1	1	1	1	1	1	1		1	1	1	1	1	1	1	1	1	1
	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20

In mathematics, multiplication is an elementary arithmetic operation. ... For other uses of 2, see 2 (disambiguation). ... This article is about the number. ... Look up four in Wiktionary, the free dictionary. ... Look up five in Wiktionary, the free dictionary. ... This article is about the mathematical number. ... Seven redirects here. ... Look up eight in Wiktionary, the free dictionary. ... This article is about the number. ... This article is about the number 10. ... 11 (eleven) is the natural number following 10 and preceding 12. ... Look up twelve in Wiktionary, the free dictionary. ... 13 (thirteen) is the natural number after 12 and before 14. ... 14 (fourteen) is the natural number following 13 and preceding 15. ... 15 (fifteen) is the natural number following 14 and preceding 16. ... 16 (sixteen) is the natural number following 15 and preceding 17. ... 17 (seventeen) is the natural number following 16 and preceding 18. ... 18 (eighteen) is the natural number following 17 and preceding 19. ... 19 (nineteen) is the natural number following 18 and preceding 20. ... Twenty redirects here. ... 21 (twenty-one) is the natural number following 20 and preceding 22. ... 22 (twenty-two) is the natural number following 21 and preceding 23. ... 23 (twenty-three) is the natural number following 22 and preceding 24. ... 24 (twenty-four) is the natural number following 23 and preceding 25. ... 25 (twenty-five) is the natural number following 24 and preceding 26. ... 50 (fifty) is the number following 49 and preceding 51. ... 100 (one hundred) (the Roman numeral is C for centum) is the natural number following 99 and preceding 101. ... Look up one thousand in Wiktionary, the free dictionary. ... In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ... “Exponent” redirects here. ...

Evolution of the glyph

Evolution of the numeral 1 from the Brahmin Indians to the Europeans I drew these characters by hand and scanned them. ...

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 Indians, who wrote 1 as a horizontal line, as is still the case in Chinese script. The Gupta wrote it as a curved line, and the Nagari sometimes added a small circle on the left (rotated a quarter turn to the right, this 9-look-alike became the present day numeral 1 in the Gujarati and Punjabi scripts). The Nepali also rotated it to the right, but kept the circle small.^[1] This eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. In some European countries (e.g., Germany) the little 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 for seven in other countries. Where the 1 is written with a long upstroke, the number 7 has a horizontal stroke through the vertical line. Chinese (written) language (pinyin: zhōngw n) written in Chinese characters The Chinese language (汉语/漢語, 华语/華語, or 中文; Pinyin: H nyǔ, Hu yǔ, or Zhōngw n) is a member of the Sino-Tibetan family of languages. ... The Gupta script was used for writing Sanskrit and is associated with the Gupta Empire of India which was a period of material prosperity and great religious and scientific developments. ... The Brahmic family is a family of abugidas used in South Asia and Southeast Asia. ... Gujarati (ગુજરાતી GujÇŽrātÄ«; also known as Gujerati, Gujarathi, Guzratee, and Guujaratee[3]) is an Indo-Aryan language descending from Sanskrit, and part of the greater Indo-European language family. ... Punjabi (also Panjabi; in GurmukhÄ«, PanjābÄ« in ShāhmukhÄ«) is the language of the Punjab regions of India and Pakistan. ... Nepali (Khaskura) is an Indo-Aryan language spoken in Nepal, Bhutan, and some parts of India and Myanmar (Burma). ... Seven redirects here. ...

While the shape of the 1 character has an ascender in most modern typefaces, in typefaces with text figures the character usually is of x-height, as, for example, in . The ascenders are the parts of the characters that lie above the midline, highlighted in red. ... “Font” redirects here. ... Hoefler Text, a contemporary font, uses hanging or old style text figures. ... In typography, the x-height or corpus size refers to the height of the lowercase letter x in any font, which is usually the same for a, c, e, m, n, o, r, s, u, v, w, and z. ... Image File history File links The numerals 1, 4 and 8 written in text figures. ...

In technology

• The resin identification code used in recycling to identify polyethylene terephthalate.

Sorted household plastic waiting to be hauled away for reprocessing. ... PETE redirects here. ...

See also

Wikimedia Commons has media related to:

1

• 0.999...
• −1

In mathematics, the recurring decimal 0. ... In mathematics, −1 is the integer greater than negative two (−2) and less than 0. ...

References