1 Explained

Number:1
Numeral:unary
Factorization:∅
Divisor:1
Roman:I, i
Greek Prefix:mono-/haplo-
Latin Prefix:uni-
Lang1:Greek numeral
Lang1 Symbol:α'
Lang2:Arabic, Kurdish, Persian, Sindhi, Urdu
Lang3:Assamese & Bengali
Lang4:Chinese numeral
Lang4 Symbol:一/弌/壹
Lang5:Devanāgarī
Lang6:Santali
Lang7:Ge'ez
Lang8 Symbol:(Ani)
Lang9:Hebrew
Lang9 Symbol:
Lang10:Japanese numeral
Lang10 Symbol:一/壱
Lang11:Kannada
Lang12:Khmer
Lang13:Armenian
Lang13 Symbol:Ա
Lang14:Malayalam
Lang14 Symbol:൧
Lang15:Meitei
Lang16:Thai
Lang17:Tamil
Lang18:Telugu
Lang19:Babylonian numeral
Lang20:Egyptian hieroglyph, Aegean numeral, Chinese counting rod
Lang21:Mayan numeral
Lang21 Symbol:•
Lang22:Morse code
Lang23:Cyrillic numerals
Lang23 Symbol:А

1 (one, unit, unity) is a number, numeral, and grapheme. It is the first and smallest positive integer of the infinite sequence of natural numbers. 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 of counting or measurement, and represents a single thing. The representation of 1 evolved from ancient Sumerian and Babylonian symbols to the modern Arabic numeral. Linguistically, in English, "one" is a determiner for singular nouns and a gender-neutral pronoun.

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. In digital technology, 1 represents the "on" state in binary code, the foundation of computing. 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, including 1, is constructed by succession, that is, by adding 1 to the previous natural number. The number 1 is the multiplicative identity of the integers, real numbers, and complex numbers, that is, any number

n

multiplied by 1 remains unchanged

1 x n=n x 1=n

. As a result, the square

12=1

, square root

\sqrt{1}=1

, and any other power of 1 is always equal to 1 itself. 1 is its own factorial

1!=1

, and 0! is also 1. These are a special case of the empty product. Although 1 meets the naïve definition of a prime number, being evenly divisible only by 1 and itself (also 1), by modern convention it is regarded as neither a prime nor a composite number.

\{0\}

, a set containing only the element 0.The unary numeral system, as used in 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 due to its difficult readability.

[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, 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 integral one, depending on the application.

\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 path-connected with no '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

See also: One (pronoun). One originates from the Old English word an, derived from the Germanic root, from the Proto-Indo-European root *oi-no- (meaning "one, unique").[1] Linguistically, one is a cardinal number used for counting and expressing the number of items in a collection of things. One is most commonly a determiner used with singular countable 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 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.[2]

Symbols and representation

History

See also: History of the Hindu–Arabic numeral system. 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 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 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 common representative glyph used in the modern Western world for the number 1 is the 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 Brahmic script of ancient India, as represented by Ashoka as a simple vertical line in his Edicts of Ashoka in c. 250 BCE.[3] 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, 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 .[4] [5] 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.[6]

The lower case "" can be considered a 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.[7] [8] [9] [10] 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 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, i.e., a base-2 numeral system with numbers represented by a sequence of 1s and 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 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 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 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 Neopythagorean philosopher 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.[11] In the philosophy of Plotinus (and that of other neoplatonists), 'The One' is the ultimate reality and source of all existence. Philo of Alexandria (20 BC – AD 50) regarded the number one as God's number, and the basis for all numbers.[12]

See also

Sources

Notes and References

  1. Web site: Online Etymology Dictionary . etymonline.com . Douglas Harper . December 30, 2013 . December 30, 2013 . https://web.archive.org/web/20131230234708/http://www.etymonline.com/index.php?term=one . live .
  2. Web site: Chrisomalis . Stephen . Numerical Adjectives, Greek and Latin Number Prefixes . The Phrontistery . February 24, 2022 . January 29, 2022 . https://web.archive.org/web/20220129005307/https://phrontistery.info/numbers.html . live .
  3. 10.3126/jie.v14i1.20077 . Evidences of Hierarchy of Brahmi Numeral System . 2018 . Acharya . Eka Ratna . Journal of the Institute of Engineering . 14 . 1 . 136–142 . free .
  4. Book: Hendel, Richard. Aspects of Contemporary Book Design. University of Iowa Press. 2013. 9781609381752. 146.
  5. Book: Katz, Joel. Designing Information: Human Factors and Common Sense in Information Design. John Wiley & Sons. 2012. 9781118420096. 82.
  6. Web site: Why Old Typewriters Lack A "1" Key. April 2, 2017. Post Haste Telegraph Company.
  7. Web site: Der allzeitfertige Rechenmeister. Christian. Köhler. November 23, 1693. Google Books. 70.
  8. Web site: Naeuw-keurig reys-boek: bysonderlijk dienstig voor kooplieden, en reysende persoonen, sijnde een trysoor voor den koophandel, in sigh begrijpende alle maate, en gewighte, Boekhouden, Wissel, Asseurantie ... : vorders hoe men ... kan reysen ... door Neederlandt, Duytschlandt, Vrankryk, Spanjen, Portugael en Italiën .... November 23, 1679. by Jan ten Hoorn. Google Books. 341.
  9. Web site: Articvli Defensionales Peremptoriales & Elisivi, Bvrgermaister vnd Raths zu Nürmberg, Contra Brandenburg, In causa die Fraiszlich Obrigkait [et]c: Produ. 7. Feb. Anno [et]c. 33]. November 23, 1586. Heußler. Google Books. 3. December 2, 2023. November 13, 2024. https://web.archive.org/web/20241113172327/https://books.google.com/books?id=UJ-VoRZUhaYC&dq=JO+JJ&pg=PA3. live.
  10. Web site: Gustavi Seleni Cryptomenytices Et Cryptographiae Libri IX.: In quibus & planißima Steganographiae a Johanne Trithemio ... magice & aenigmatice olim conscriptae, Enodatio traditur; Inspersis ubique Authoris ac Aliorum, non contemnendis inventis. Braunschweig-Lüneburg. August (Herzog). November 23, 1624. Johann & Heinrich Stern. Google Books. 285.
  11. From Abacus to Algorism: Theory and Practice in Medieval Arithmetic. The British Journal for the History of Science. 10. 2. July 1, 1977. Abstract. 10.1017/S0007087400015375. Cambridge University Press. British Society for the History of Science. 145065082. May 16, 2021. May 16, 2021. https://web.archive.org/web/20210516110812/https://www.cambridge.org/core/journals/british-journal-for-the-history-of-science/article/abs/from-abacus-to-algorism-theory-and-practice-in-medieval-arithmetic/7DFF144C90C127E715CA40083254E601#access-block. live. subscription.
  12. "De Allegoriis Legum", ii.12 [i.66]

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