1&1 All Net Flat Young Lte

Natural number

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Primal	ane
Ordinal	1st (start)
Numeral arrangement	unary
Factorization	∅
Divisors	1
Greek numeral	Α´
Roman numeral	I, i
Greek prefix	mono-/haplo-
Latin prefix	uni-
Binary	1two
Ternary	13
Senary	16
Octal	1eight
Duodecimal	i12
Hexadecimal	116
Greek numeral	α'
Arabic, Kurdish, Western farsi, Sindhi, Urdu	١
Assamese & Bengali	১
Chinese numeral	一/弌/壹
Devanāgarī	१
Ge'ez	፩
Georgian	Ⴀ/ⴀ/ა(Ani)
Hebrew	א
Japanese numeral	一/壱
Kannada	೧
Khmer	១
Malayalam	൧
Thai	๑
Tamil	௧
Telugu	೧
Counting rod	𝍠

ane (one, likewise chosen unit of measurement, and unity) is a number and a numerical digit used to represent that number in numerals. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length ane. In conventions of sign where nothing is considered neither positive nor negative, 1 is the first and smallest positive integer.^[one] It is also sometimes considered the start of the infinite sequence of natural numbers, followed by 2, although past other definitions i is the second natural number, post-obit 0.

The fundamental mathematical holding of ane is to be a multiplicative identity, pregnant that any number multiplied past 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is ofttimes denoted 1, even if it is non a number. 1 is by convention not considered a prime; although universally accustomed today, this fact was controversial until the mid-20th century. Additionally, 1 is the smallest possible difference between two distinct natural numbers.

The unique mathematical properties of the number have led to its unique uses in other fields, ranging from science to sports. It usually denotes the outset, leading, or acme affair in a group.

Etymology

The word i tin can exist used as a noun, an adjective, and a pronoun.^[2]

It comes from the English language word an,^[ii] which comes from the Proto-Germanic root *ainaz.^[2] The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no-.^[2]

Compare the Proto-Germanic root *ainaz to Sometime Frisian an, Gothic ains, Danish en, Dutch een, German language eins and Old Norse einn.

Compare the Proto-Indo-European root *oi-no- (which means "one, single"^[2]) to Greek oinos (which means "ace" on dice^[2]), Latin unus (one^[2]), Onetime Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin and Breton un (1^[ii]).

As a number

One, sometimes referred to as unity,^{[3] [1]} is the first non-zero natural number. It is thus the integer afterwards zero.

Whatever number multiplied by one remains that number, as one is the identity for multiplication. As a upshot, 1 is its own factorial, its ain foursquare and square root, its own cube and cube root, and then on. One is also the result of the empty product, as any number multiplied by one is itself. It is also the only natural number that is neither composite nor prime with respect to division, merely is instead considered a unit of measurement (significant of ring theory).

As a digit

The 24-hour tower clock in Venice, using J as a symbol for 1

This Woodstock typewriter from the 1940s lacks a carve up fundamental for the numeral ane.

Hoefler Text, a typeface designed in 1991, represents the numeral 1 every bit similar to a small-caps I.

The glyph used today in the Western globe to represent the number 1, a vertical line, frequently with a serif at the peak 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. It was transmitted to Europe via the Maghreb and Andalusia during the Centre Ages, through scholarly works written in Standard arabic.

In some countries, the serif at the pinnacle is sometimes extended into a long upstroke, sometimes as long equally the vertical line, which tin can lead to confusion with the glyph used for 7 in other countries. In styles in which the digit one is written with a long upstroke, the digit 7 is often written with a horizontal stroke through the vertical line, to disambiguate them. Styles that do not use the long upstroke on digit ane unremarkably do not utilize the horizontal stroke through the vertical of the digit 7 either.

While the shape of the character for the digit 1 has an ascender in almost modern typefaces, in typefaces with text figures, the glyph unremarkably is of ten-height, as, for case, in .

Many older typewriters lack a divide key for 1, using the lowercase letter of the alphabet 50 or uppercase I instead. It is possible to find cases when the uppercase J is used, though it may exist for decorative purposes. In some typefaces, different glyphs are used for I and 1, but the numeral i resembles a pocket-size caps version of I, with parallel serifs at top and lesser, with the capital I being full-height.

Mathematics

Definitions

Mathematically, 1 is:

• in arithmetic (algebra) and calculus, the natural number that follows 0 and the multiplicative identity element of the integers, real numbers and complex numbers;
• more by and large, in algebra, the multiplicative identity (also called unity), usually of a group or a ring.

Formalizations of the natural numbers have their ain representations of 1. In the Peano axioms, ane is the successor of 0. In Principia Mathematica, it is defined every bit the set of all singletons (sets with one element), and in the Von Neumann cardinal assignment of natural numbers, it is defined as the set {0}.

In a multiplicative group or monoid, the identity element is sometimes denoted 1, but eastward (from the German Einheit, "unity") is also traditional. However, i is especially common for the multiplicative identity of a ring, i.e., when an add-on and 0 are also present. When such a ring has feature n non equal to 0, the element called 1 has the belongings that n1 = 1n = 0 (where this 0 is the additive identity of the ring). Important examples are finite fields.

By definition, 1 is the magnitude, absolute value, or norm of a unit complex number, unit vector, and a unit matrix (more than usually called an identity matrix). Note that the term unit matrix is sometimes used to mean something quite different.

By definition, i is the probability of an consequence that is absolutely or almost sure to occur.

In category theory, i is sometimes used to announce the concluding object of a category.

In number theory, 1 is the value of Legendre's abiding, which was introduced in 1808 by Adrien-Marie Legendre in expressing the asymptotic beliefs of the prime-counting function. Legendre'south constant was originally conjectured to be approximately 1.08366, simply was proven to equal exactly 1 in 1899.

Properties

Tallying is ofttimes referred to every bit "base 1", since just one marking – the tally itself – is needed. This is more than formally referred to as a unary numeral organization. Unlike base ii or base 10, this is not a positional notation.

Since the base 1 exponential office (ane ^x ) always equals 1, its inverse does non exist (which would be called the logarithm base 1 if it did be).

There are 2 ways to write the real number 1 every bit a recurring decimal: as ane.000..., and every bit 0.999.... 1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few.

In many mathematical and engineering problems, numeric values are typically normalized to fall inside the unit of measurement interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters. Likewise, vectors are ofttimes normalized into unit of measurement vectors (i.e., vectors of magnitude one), because these often accept more desirable properties. Functions, too, are ofttimes normalized by the status that they have integral one, maximum value one, or foursquare integral one, depending on the application.

Because of the multiplicative identity, if f(ten) is a multiplicative office, so f(1) must be equal to 1.

It is also the first and 2d number in the Fibonacci sequence (0 being the zeroth) and is the first number in many other mathematical sequences.

The definition of a field requires that 1 must not be equal to 0. Thus, there are no fields of feature i. Nevertheless, abstract algebra can consider the field with ane element, which is not a singleton and is not a set up at all.

i is the well-nigh mutual leading digit in many sets of data, a consequence of Benford'due south law.

one is the only known Tamagawa number for a but connected algebraic group over a number field.

The generating function that has all coefficients 1 is given by

${\displaystyle {\frac {i}{1-x}}=one+x+x^{2}+ten^{iii}+\ldots }$

This power series converges and has finite value if and only if ${\displaystyle |x|<1}$ .

Primality

1 is past convention neither a prime number nor a composite number, simply a unit of measurement (meaning of ring theory) like −ane and, in the Gaussian integers, i and −i.

The fundamental theorem of arithmetic guarantees unique factorization over the integers just upwards to units. For example, four = ii² , but if units are included, is also equal to, say, (−1)⁶ × 1²³ × 2², among infinitely many similar "factorizations".

ane appears to meet the naïve definition of a prime number, being evenly divisible merely by one and itself (also one). As such, some mathematicians considered it a prime number every bit late as the centre of the 20th century, but mathematical consensus has by and large and since then universally been to exclude it for a diverseness of reasons (such as complicating the fundamental theorem of arithmetic and other theorems related to prime numbers).

1 is the but positive integer divisible past exactly i positive integer, whereas prime numbers are divisible past exactly two positive integers, composite numbers are divisible past more than than two positive integers, and zero is divisible by all positive integers.

Table of basic calculations

Multiplication	ane	ii	iii	4	5	6	7	8	9	ten		11	12	13	14	15	16	17	18	19	xx		21	22	23	24	25		50	100	1000
1 × x	one	ii	iii	iv	5	six	7	8	9	10		xi	12	xiii	fourteen	15	sixteen	17	eighteen	xix	20		21	22	23	24	25		50	100	1000

Division	1	ii	3	4	v	6	7	8	nine	10		11	12	13	14	xv
i ÷ x	1	0.v	0.3	0.25	0.2	0.16	0.142857	0.125	0.1	0.one		0.09	0.083	0.076923	0.0714285	0.06
10 ÷ 1	one	2	3	4	5	vi	seven	8	9	10		xi	12	13	14	xv

Exponentiation	ane	2	3	iv	v	6	7	8	9	x		xi	12	13	14	15	16	17	eighteen	19	twenty
1 x	1	1	1	one	ane	1	one	one	1	1		1	1	ane	1	one	1	1	ane	1	1
10 1	one	2	3	four	five	6	7	viii	9	10		11	12	13	14	15	xvi	17	xviii	19	20

In engineering

• The resin identification code used in recycling to identify polyethylene terephthalate.^[4]
• The ITU country code for the Due north American Numbering Programme area, which includes the The states, Canada, and parts of the Caribbean.
• A binary code is a sequence of one and 0 that is used in computers for representing whatsoever kind of data.
• In many physical devices, 1 represents the value for "on", which means that electricity is flowing.^{[5] [six]}
• The numerical value of truthful in many programming languages.
• one is the ASCII code of "Start of Header".

In science

• Dimensionless quantities are besides known as quantities of dimension one.
• ane is the atomic number of hydrogen.
• +1 is the electric charge of positrons and protons.
• Group ane of the periodic table consists of the alkali metals.
• Period one of the periodic table consists of just two elements, hydrogen and helium.
• The dwarf planet Ceres has the small-scale-planet designation 1 Ceres considering information technology was the first asteroid to be discovered.
• The Roman numeral I often stands for the first-discovered satellite of a planet or minor planet (such as Neptune I, a.k.a. Triton). For some before discoveries, the Roman numerals originally reflected the increasing distance from the primary instead.

In philosophy

In the philosophy of Plotinus (and that of other neoplatonists), The I is the ultimate reality and source of all existence.^[7] Philo of Alexandria (20 BC – Advertisement 50) regarded the number 1 every bit God'due south number, and the basis for all numbers ("De Allegoriis Legum," ii.12 [i.66]).

The Neopythagorean philosopher Nicomachus of Gerasa affirmed that one is not a number, but the source of number. He also believed the number two is the apotheosis of the origin of otherness. His number theory was recovered by Boethius in his Latin translation of Nicomachus's treatise Introduction to Arithmetic.^[8]

In sports

In many professional sports, the number 1 is assigned to the player who is kickoff or leading in some respect, or otherwise important; the number is printed on his sports compatible or equipment. This is the pitcher in baseball, the goalkeeper in association football game (soccer), the starting fullback in most of rugby league, the starting loosehead prop in rugby marriage and the previous year'south world champion in Formula 1. 1 may be the lowest possible thespian number, like in the American–Canadian National Hockey League (NHL) since the 1990s^{[ when? ]} or in American football.

In other fields

• Number Ane is Royal Navy informal usage for the chief executive officer of a ship, the captain's deputy responsible for discipline and all normal performance of a send and its crew.
• 1 is the value of an ace in many playing carte games, such equally cribbage.
• Listing of highways numbered 1
• Listing of public transport routes numbered 1
• ane is frequently used to denote the Gregorian calendar calendar month of Jan.
• 1 CE, the first yr of the Common Era
• 01, the quondam dialling code for Greater London (now 020)
• For Pythagorean numerology (a pseudoscience), the number 1 is the number that means beginning, new ancestry, new cycles, it is a unique and absolute number.
• PRS One, a German paraglider design
• +1 is the lawmaking for international telephone calls to countries in the N American Numbering Program.
• In some countries, a street accost of "1" is considered prestigious and developers will attempt to obtain such an accost for a building, to the point of lobbying for a street or portion of a street to be renamed, even if this makes the address less useful for wayfinding. The structure of a new street to serve the development may also provide the possibility of a "1" address. An example of such an address is the Apple Campus, located at 1 Infinite Loop, Cupertino, California.

See as well

• −i
• +1 (disambiguation)
• List of mathematical constants
• One (discussion)
• Root of unity
• Listing of highways numbered 1

References

1. ^ ^{a b} Weisstein, Eric W. "1". mathworld.wolfram.com . Retrieved 2020-08-10 .
2. ^ ^{a b c d e f g h} "Online Etymology Lexicon". etymonline.com. Douglas Harper.
3. ^ Skoog, Douglas. Principles of Instrumental Assay. Brooks/Cole, 2007, p. 758.
4. ^ "Plastic Packaging Resins" (PDF). American Chemistry Council. Archived from the original (PDF) on 2011-07-21.
5. ^ Woodford, Chris (2006), Digital Engineering science, Evans Brothers, p. 9, ISBN978-0-237-52725-ix
6. ^ Godbole, Achyut Due south. (1 September 2002), Information Comms & Networks, Tata McGraw-Hill Education, p. 34, ISBN978-ane-259-08223-8
7. ^ Olson, Roger (2017). The Essentials of Christian Thought: Seeing Reality through the Biblical Story. Zondervan Bookish. ISBN9780310521563.
8. ^ British Society for the History of Science (July 1, 1977). "From Abacus to Algorism: Theory and Practise in Medieval Arithmetic". The British Periodical for the History of Science. Cambridge University PRess. 10 (2): Abstract. doi:10.1017/S0007087400015375. S2CID 145065082. Retrieved May sixteen, 2021.

External links

• The Number 1
• The Positive Integer 1
• Prime curiosities: 1

1&1 All Net Flat Young Lte,

Source: https://en.wikipedia.org/wiki/1

Posted by: reedbuls1994.blogspot.com

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