2012–13 Cal Poly Mustangs Men's Basketball Team
   HOME

TheInfoList



OR:

1 (one, unit, unity) is a
number A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...
, numeral, and
glyph A glyph ( ) is any kind of purposeful mark. In typography, a glyph is "the specific shape, design, or representation of a character". It is a particular graphical representation, in a particular typeface, of an element of written language. A ...
. It is the first and smallest
positive integer In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positiv ...
of the infinite sequence of
natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
s. This fundamental property has led to its unique uses in other fields, ranging from science to sports, where it commonly denotes the first, leading, or top thing in a group. 1 is the
unit Unit may refer to: General measurement * Unit of measurement, a definite magnitude of a physical quantity, defined and adopted by convention or by law **International System of Units (SI), modern form of the metric system **English units, histo ...
of
counting Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for ever ...
or
measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to ...
, a determiner for singular nouns, and a gender-neutral pronoun. Historically, the representation of 1 evolved from ancient Sumerian and Babylonian symbols to the modern Arabic numeral. In mathematics, 1 is the multiplicative identity, meaning that any number multiplied by 1 equals the same number. 1 is by convention not considered a
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
. In
digital technology Digital technology may refer to: * Application of digital electronics * Any significant piece of knowledge from information technology Information technology (IT) is a set of related fields within information and communications technology (IC ...
, 1 represents the "on" state in
binary code A binary code represents plain text, text, instruction set, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number, binary number system. The binary cod ...
, the foundation of
computing Computing is any goal-oriented activity requiring, benefiting from, or creating computer, computing machinery. It includes the study and experimentation of algorithmic processes, and the development of both computer hardware, hardware and softw ...
. Philosophically, 1 symbolizes the ultimate reality or source of existence in various traditions.


In mathematics

The number 1 is the first natural number after 0. Each
natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
, including 1, is constructed by
succession Succession is the act or process of following in order or sequence. Governance and politics *Order of succession, in politics, the ascension to power by one ruler, official, or monarch after the death, resignation, or removal from office of ...
, that is, by adding 1 to the previous natural number. The number 1 is the
multiplicative identity In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. For example, 0 is an identity element of the addition of real numbers. This concept is use ...
of the
integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
s,
real number In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...
s, and
complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...
s, that is, any number n multiplied by 1 remains unchanged (1\times n = n\times 1 = n). As a result, the
square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...
(1^2=1),
square root In mathematics, a square root of a number is a number such that y^2 = x; in other words, a number whose ''square'' (the result of multiplying the number by itself, or y \cdot y) is . For example, 4 and −4 are square roots of 16 because 4 ...
(\sqrt = 1), and any other power of 1 is always equal to 1 itself. 1 is its own
factorial In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times ...
(1!=1), and 0! is also 1. These are a special case of the
empty product In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplication, multiplying no factors. It is by convention equal to the multiplicative identity (assuming there is an identity for the multiplication operat ...
. Although 1 meets the naïve definition of a
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
, being evenly divisible only by 1 and itself (also 1), by modern convention it is regarded as neither a
prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
nor a
composite number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...
. Different mathematical constructions of the natural numbers represent 1 in various ways. In
Giuseppe Peano Giuseppe Peano (; ; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much Mathematical notati ...
's original formulation of the
Peano axioms In mathematical logic, the Peano axioms (, ), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th-century Italian mathematician Giuseppe Peano. These axioms have been used nea ...
, a set of postulates to define the natural numbers in a precise and logical way, 1 was treated as the starting point of the sequence of natural numbers. Peano later revised his axioms to begin the sequence with 0. In the
Von Neumann cardinal assignment The von Neumann cardinal assignment is a cardinal assignment that uses ordinal numbers. For a well-orderable set ''U'', we define its cardinal number to be the smallest ordinal number equinumerous to ''U'', using the von Neumann definition of a ...
of natural numbers, where each number is defined as a
set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...
that contains all numbers before it, 1 is represented as the
singleton Singleton may refer to: Sciences, technology Mathematics * Singleton (mathematics), a set with exactly one element * Singleton field, used in conformal field theory Computing * Singleton pattern, a design pattern that allows only one instance ...
\, a set containing only the element 0. The unary numeral system, as used in Tally mark, tallying, is an example of a "base-1" number system, since only one mark – the tally itself – is needed. While this is the simplest way to represent the natural numbers, base-1 is rarely used as a practical base for
counting Counting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for ever ...
due to its difficult readability. In many mathematical and engineering problems, numeric values are typically Normalized solution (mathematics), normalized to fall within the unit interval ([0,1]), where 1 represents the maximum possible value. For example, by definition 1 is the probability of an event that is absolutely or almost certain to occur. Likewise, vector space, vectors are often normalized into unit vectors (i.e., vectors of magnitude one), because these often have more desirable properties. Functions are often normalized by the condition that they have integral one, maximum value one, or square integrable, square integral one, depending on the application. 1 is the value of Legendre's constant, introduced in 1808 by Adrien-Marie Legendre to express the Asymptotic analysis, asymptotic behavior of the prime-counting function. The Weil's conjecture on Tamagawa numbers states that the Tamagawa number \tau(G), a geometrical measure of a connected linear algebraic group over a global number field, is 1 for all simply connected groups (those that are Homotopical connectivity, path-connected with no 'Homotopical connectivity#Definition using holes, holes'). 1 is the most common leading digit in many sets of real-world numerical data. This is a consequence of Benford’s law, which states that the probability for a specific leading digit d is \log_ \left(\frac \right) . The tendency for real-world numbers to grow exponentially or logarithmically biases the distribution towards smaller leading digits, with 1 occurring approximately 30% of the time.


As a word

''One'' originates from the Old English word ''an'', derived from the Germanic languages, Germanic root , from the Proto-Indo-European root ''*oi-no-'' (meaning "one, unique"). Linguistically, ''one'' is a Cardinal numeral, cardinal number used for counting and expressing the number of items in a collection of things. ''One'' is most commonly a English determiners, determiner used with Grammatical number, singular countable English nouns, nouns, as in ''one day at a time''. The determiner has two senses: numerical one (''I have one apple'') and singulative one (''one day I'll do it''). ''One'' is also a gender-neutral One (pronoun), pronoun used to refer to an unspecified person or to people in general as in ''one should take care of oneself''. Words that derive their meaning from ''one'' include ''alone'', which signifies ''all one'' in the sense of being by oneself, ''none'' meaning ''not one'', ''once'' denoting ''one time'', and ''atone'' meaning to become ''at one'' with the someone. Combining ''alone'' with ''only'' (implying ''one-like'') leads to ''lonely'', conveying a sense of solitude. Other common numeral prefixes for the number 1 include ''uni-'' (e.g., unicycle, universe, unicorn), ''sol-'' (e.g., solo dance), derived from Latin, or ''mono-'' (e.g., monorail, monogamy, monopoly) derived from Greek.


Symbols and representation


History

Among the earliest known records of a numeral system, is the Sumerian decimal-sexagesimal system on clay tablets dating from the first half of the 3rd millennium BC, third millennium BCE. Archaic Sumerian numerals for 1 and 60 both consisted of horizontal semi-circular symbols, by , the older Sumerian curviform numerals were replaced with cuneiform symbols, with 1 and 60 both represented by the same mostly vertical symbol. The Sumerian cuneiform system is a direct ancestor to the Eblaite and Assyro-Babylonian Semitic languages, Semitic cuneiform decimal systems. Surviving Babylonian documents date mostly from Old Babylonian () and the Seleucid () eras. The Babylonian cuneiform script notation for numbers used the same symbol for 1 and 60 as in the Sumerian system. The most commonly used glyph in the modern Western world to represent the number 1 is the Arabic numerals, Arabic numeral, a vertical line, often with a serif at the top and sometimes a short horizontal line at the bottom. It can be traced back to the Brahmi numerals, Brahmic script of ancient India, as represented by Ashoka as a simple vertical line in his Edicts of Ashoka in c. 250 BCE. This script's numeral shapes were transmitted to Europe via the Maghreb and Al-Andalus during the Middle Ages The Arabic numeral, and other glyphs used to represent the number one (e.g., Roman numeral ( ), Chinese numeral ()) are logograms. These symbols directly represent the concept of 'one' without breaking it down into phonetic components.


Modern typefaces

In modern typefaces, the shape of the character for the digit 1 is typically typeset as a ''lining figure'' with an Ascender (typography), ascender, such that the digit is the same height and width as a capital letter. However, in typefaces with text figures (also known as ''Old style numerals'' or ''non-lining figures''), the glyph usually is of x-height and designed to follow the rhythm of the lowercase, as, for example, in . In many typefaces with text figures, the numeral 1 features parallel serifs at the top and bottom, resembling a small caps version of the Roman numeral . Many older typewriters do not have a dedicated key for the numeral 1, requiring the use of the lowercase letter ''L'' or uppercase ''I'' as substitutes. The lower case "" can be considered a Swash (typography), swash variant of a lower-case Roman numeral "", often employed for the final of a "lower-case" Roman numeral. It is also possible to find historic examples of the use of ''j'' or ''J'' as a substitute for the Arabic numeral 1. In German, the serif at the top may be extended into a long upstroke as long as the vertical line. This variation can lead to confusion with the glyph used for 7, seven in other countries and so to provide a visual distinction between the two the digit 7 may be written with a horizontal stroke through the vertical line.


In other fields

In digital technology, data is represented by
binary code A binary code represents plain text, text, instruction set, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often "0" and "1" from the binary number, binary number system. The binary cod ...
, i.e., a radix, base-2 numeral system with numbers represented by a sequence of 1s and 0 (number), 0s. Digitised data is represented in physical devices, such as computers, as pulses of electricity through switching devices such as transistors or logic gates where "1" represents the value for "on". As such, the numerical value of Boolean data type, true is equal to 1 in many programming languages. In lambda calculus and computability theory, natural numbers are represented by Church encoding as functions, where the Church numeral for 1 is represented by the function f applied to an argument x once . In physics, selected physical constants are set to 1 in natural unit systems in order to simplify the form of equations; for example, in Planck units the speed of light equals 1. Dimensionless quantities are also known as 'quantities of dimension one'. In quantum mechanics, the normalization condition for wavefunctions requires the integral of a wavefunction's squared modulus to be equal to 1. In chemistry, hydrogen, the first element of the periodic table and the most Abundance of the elements, abundant element in the known universe, has an atomic number of 1. Group 1 of the periodic table consists of hydrogen and the alkali metals. In philosophy, the number 1 is commonly regarded as a symbol of unity, often representing God or the universe in Monotheism, monotheistic traditions. The Pythagoreans considered the numbers to be plural and therefore did not classify 1 itself as a number, but as the origin of all numbers. In their number philosophy, where odd numbers were considered male and even numbers female, 1 was considered neutral capable of transforming even numbers to odd and vice versa by addition. The Neopythagoreanism, Neopythagorean philosopher Nicomachus, Nicomachus of Gerasa's number treatise, as recovered by Boethius in the Latin translation ''Introduction to Arithmetic'', affirmed that one is not a number, but the source of number. In the philosophy of Plotinus (and that of other neoplatonists), 'The One' is the ultimate reality and source of all existence. Philo#Numbers, Philo of Alexandria (20 BC – AD 50) regarded the number one as God's number, and the basis for all numbers."De Allegoriis Legum", ii.12 [i.66]


See also

*−1 *


References


Sources

* * * * * * * * * * * * * * * * *. * * * * * * * * * * * * * * * * * * {{DEFAULTSORT:1 (Number) 1 (number), Integers