List of numbers
Template:Short description Template:Pp {{#invoke:Hatnote|hatnote}}{{#ifeq:||}} This is a list of notable numbers and articles about notable numbers. The list does not contain all numbers in existence as most of the number sets are infinite. Numbers may be included in the list based on their mathematical, historical or cultural notability, but all numbers have qualities that could arguably make them notable. Even the smallest "uninteresting" number is paradoxically interesting for that very property. This is known as the interesting number paradox.
The definition of what is classed as a number is rather diffuse and based on historical distinctions. For example, the pair of numbers (3,4) is commonly regarded as a number when it is in the form of a complex number (3+4i), but not when it is in the form of a vector (3,4). This list will also be categorized with the standard convention of types of numbers.
This list focuses on numbers as mathematical objects and is not a list of numerals, which are linguistic devices: nouns, adjectives, or adverbs that designate numbers. The distinction is drawn between the number five (an abstract object equal to 2+3), and the numeral five (the noun referring to the number).
Natural numbersEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} Natural numbers are a subset of the integers and are of historical and pedagogical value as they can be used for counting and often have ethno-cultural significance (see below). Beyond this, natural numbers are widely used as a building block for other number systems including the integers, rational numbers and real numbers. Natural numbers are those used for counting (as in "there are six (6) coins on the table") and ordering (as in "this is the third (3rd) largest city in the country"). In common language, words used for counting are "cardinal numbers" and words used for ordering are "ordinal numbers". Defined by the Peano axioms, the natural numbers form an infinitely large set. Often referred to as "the naturals", the natural numbers are usually symbolised by a boldface Template:Math (or blackboard bold <math>\mathbb{\N}</math>, Unicode Template:Unichar).
The inclusion of 0 in the set of natural numbers is ambiguous and subject to individual definitions. In set theory and computer science, 0 is typically considered a natural number. In number theory, it usually is not. The ambiguity can be solved with the terms "non-negative integers", which includes 0, and "positive integers", which does not.
Natural numbers may be used as cardinal numbers, which may go by various names. Natural numbers may also be used as ordinal numbers.
Mathematical significanceEdit
Natural numbers may have properties specific to the individual number or may be part of a set (such as prime numbers) of numbers with a particular property.Template:Collapsible list
Cultural or practical significanceEdit
Along with their mathematical properties, many integers have cultural significance<ref>Template:Cite journal</ref> or are also notable for their use in computing and measurement. As mathematical properties (such as divisibility) can confer practical utility, there may be interplay and connections between the cultural or practical significance of an integer and its mathematical properties.
Classes of natural numbersEdit
Subsets of the natural numbers, such as the prime numbers, may be grouped into sets, for instance based on the divisibility of their members. Infinitely many such sets are possible. A list of notable classes of natural numbers may be found at classes of natural numbers.
Prime numbersEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} A prime number is a positive integer which has exactly two divisors: 1 and itself.
The first 100 prime numbers are:
2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 |
31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 |
73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 |
127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 |
179 | 181 | 191 | 193 | 197 | 199 | 211 | 223 | 227 | 229 |
233 | 239 | 241 | 251 | 257 | 263 | 269 | 271 | 277 | 281 |
283 | 293 | 307 | 311 | 313 | 317 | 331 | 337 | 347 | 349 |
353 | 359 | 367 | 373 | 379 | 383 | 389 | 397 | 401 | 409 |
419 | 421 | 431 | 433 | 439 | 443 | 449 | 457 | 461 | 463 |
467 | 479 | 487 | 491 | 499 | 503 | 509 | 521 | 523 | 541 |
Highly composite numbersEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}}
A highly composite number (HCN) is a positive integer with more divisors than any smaller positive integer. They are often used in geometry, grouping and time measurement.
The first 20 highly composite numbers are:
1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560
Perfect numbersEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}}
A perfect number is an integer that is the sum of its positive proper divisors (all divisors except itself).
The first 10 perfect numbers:
IntegersEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}}
The integers are a set of numbers commonly encountered in arithmetic and number theory. There are many subsets of the integers, including the natural numbers, prime numbers, perfect numbers, etc. Many integers are notable for their mathematical properties. Integers are usually symbolised by a boldface Template:Math (or blackboard bold <math>\mathbb{\Z}</math>, Unicode Template:Unichar); this became the symbol for the integers based on the German word for "numbers" (Zahlen).
Notable integers include −1, the additive inverse of unity, and 0, the additive identity.
As with the natural numbers, the integers may also have cultural or practical significance. For instance, −40 is the equal point in the Fahrenheit and Celsius scales.
SI prefixesEdit
One important use of integers is in orders of magnitude. A power of 10 is a number 10k, where k is an integer. For instance, with k = 0, 1, 2, 3, ..., the appropriate powers of ten are 1, 10, 100, 1000, ... Powers of ten can also be fractional: for instance, k = -3 gives 1/1000, or 0.001. This is used in scientific notation, real numbers are written in the form m × 10n. The number 394,000 is written in this form as 3.94 × 105.
Integers are used as prefixes in the SI system. A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol. The prefix kilo-, for example, may be added to gram to indicate multiplication by one thousand: one kilogram is equal to one thousand grams. The prefix milli-, likewise, may be added to metre to indicate division by one thousand; one millimetre is equal to one thousandth of a metre.
Value | 1000m | Name | Symbol |
---|---|---|---|
Template:Gaps | 10001 | Kilo | k |
Template:Gaps | 10002 | Mega | M |
Template:Gaps | 10003 | Giga | G |
Template:Gaps | 10004 | Tera | T |
Template:Gaps | 10005 | Peta | P |
Template:Gaps | 10006 | Exa | E |
Template:Gaps | 10007 | Zetta | Z |
Template:Gaps | 10008 | Yotta | Y |
Template:Gaps | 10009 | Ronna | R |
Template:Gaps | 100010 | Quetta | Q |
Rational numbersEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} A rational number is any number that can be expressed as the quotient or fraction Template:Math of two integers, a numerator Template:Math and a non-zero denominator Template:Math.<ref name="Rosen">Template:Cite book</ref> Since Template:Math may be equal to 1, every integer is trivially a rational number. The set of all rational numbers, often referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by a boldface Template:Math (or blackboard bold <math>\mathbb{Q}</math>, Unicode Template:Unichar);<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> it was thus denoted in 1895 by Giuseppe Peano after quoziente, Italian for "quotient".
Rational numbers such as 0.12 can be represented in infinitely many ways, e.g. zero-point-one-two (0.12), three twenty-fifths (Template:Sfrac), nine seventy-fifths (Template:Sfrac), etc. This can be mitigated by representing rational numbers in a canonical form as an irreducible fraction.
A list of rational numbers is shown below. The names of fractions can be found at numeral (linguistics).
Decimal expansion | Fraction | Notability |
---|---|---|
1.0 | Template:Sfrac | One is the multiplicative identity. One is a rational number, as it is equal to 1/1. |
1 | ||
−0.083 333... | Template:Sfrac | The value assigned to the series 1+2+3... by zeta function regularization and Ramanujan summation. |
0.5 | Template:Sfrac | One half occurs commonly in mathematical equations and in real world proportions. One half appears in the formula for the area of a triangle: Template:Sfrac × base × perpendicular height and in the formulae for figurate numbers, such as triangular numbers and pentagonal numbers. |
3.142 857... | Template:Sfrac | A widely used approximation for the number <math>\pi</math>. It can be proven that this number exceeds <math>\pi</math>. |
0.166 666... | Template:Sfrac | One sixth. Often appears in mathematical equations, such as in the sum of squares of the integers and in the solution to the Basel problem. |
Real numbersEdit
Real numbers are least upper bounds of sets of rational numbers that are bounded above, or greatest lower bounds of sets of rational numbers that are bounded below, or limits of convergent sequences of rational numbers. Real numbers that are not rational numbers are called irrational numbers. The real numbers are categorised as algebraic numbers (which are the root of a polynomial with rational coefficients) or transcendental numbers, which are not; all rational numbers are algebraic.
Algebraic numbersEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} Template:Sticky header
Name | Expression | Decimal expansion | Notability |
---|---|---|---|
Golden ratio conjugate (<math>\Phi</math>) | <math>\frac{\sqrt{5}-1}{2}</math> | Template:Val | Reciprocal of (and one less than) the golden ratio. |
Twelfth root of two | <math>\sqrt[12]{2}</math> | Template:Val | Proportion between the frequencies of adjacent semitones in the 12 tone equal temperament scale. |
Cube root of two | <math>\sqrt[3]{2}</math> | Template:Val | Length of the edge of a cube with volume two. See doubling the cube for the significance of this number. |
Conway's constant | (cannot be written as expressions involving integers and the operations of addition, subtraction, multiplication, division, and the extraction of roots) | Template:Val | Defined as the unique positive real root of a certain polynomial of degree 71. The limit ratio between subsequent numbers in the binary Look-and-say sequence (Template:OEIS2C). |
Plastic ratio | <math>\sqrt[3]{\frac{1}{2} +\frac{1}{6} \sqrt{\frac{23}{3}}} +\sqrt[3]{\frac{1}{2} -\frac{1}{6} \sqrt{\frac{23}{3}}}</math> | Template:Val | The only real solution of <math>x^3 = x + 1</math>.(Template:OEIS2C) The limit ratio between subsequent numbers in the Van der Laan sequence. (Template:OEIS2C) |
Square root of two | <math>\sqrt{2}</math> | Template:Val | Template:Sqrt = 2 sin 45° = 2 cos 45° Square root of two a.k.a. Pythagoras' constant. Ratio of diagonal to side length in a square. Proportion between the sides of paper sizes in the ISO 216 series (originally DIN 476 series). |
Supergolden ratio | <math>\dfrac{1 +\sqrt[3]{\dfrac{29 +3\sqrt{3 \cdot 31}}{2}} +\sqrt[3]{\dfrac{29 -3\sqrt{3 \cdot 31}}{2}}}{3}</math> | Template:Val | The only real solution of <math>x^3 = x^2 + 1</math>.(Template:OEIS2C) The limit ratio between subsequent numbers in Narayana's cows sequence. (Template:OEIS2C) |
Triangular root of 2 | <math>\frac{\sqrt{17}-1}{2}</math> | Template:Val | |
Golden ratio (φ) | <math>\frac{\sqrt{5}+1}{2}</math> | Template:Val | The larger of the two real roots of x2 = x + 1. |
Square root of three | <math>\sqrt{3}</math> | Template:Val | Template:Sqrt = 2 sin 60° = 2 cos 30° . A.k.a. the measure of the fish or Theodorus' constant. Length of the space diagonal of a cube with edge length 1. Altitude of an equilateral triangle with side length 2. Altitude of a regular hexagon with side length 1 and diagonal length 2. |
Tribonacci constant | <math>\frac{1 +\sqrt[3]{19 +3\sqrt{3 \cdot 11}} +\sqrt[3]{19 -3\sqrt{3 \cdot 11}}}{3}</math> | Template:Val | The only real solution of <math>x^3 = x^2 + x + 1</math>.(Template:OEIS2C) The limit ratio between subsequent numbers in the Tribonacci sequence.(Template:OEIS2C) Appears in the volume and coordinates of the snub cube and some related polyhedra. |
Supersilver ratio | <math>\dfrac{2 +\sqrt[3]{\dfrac{43 +3\sqrt{3 \cdot 59}}{2}} +\sqrt[3]{\dfrac{43 -3\sqrt{3 \cdot 59}}{2}}}{3}</math> | Template:Val | The only real solution of <math>x^3 = 2x^2 + 1</math>.(Template:OEIS2C) The limit ratio between subsequent numbers in the third-order Pell sequence. (Template:OEIS2C) |
Square root of five | <math>\sqrt{5}</math> | Template:Val | Length of the diagonal of a 1 × 2 rectangle. |
Silver ratio (δS) | <math>\sqrt{2}+1</math> | Template:Val | The larger of the two real roots of x2 = 2x + 1. Altitude of a regular octagon with side length 1. |
Bronze ratio (S3) | <math>\frac{\sqrt{13}+3}{2}</math> | Template:Val | The larger of the two real roots of x2 = 3x + 1. |
Transcendental numbersEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} Template:Sticky header
Name | Symbol
or Formula |
Decimal expansion | Notes and notability | |
---|---|---|---|---|
Gelfond's constant | <math>e^{\pi}</math> | Template:Val... | ||
Ramanujan's constant | <math>e^{\pi\sqrt{163}}</math> | Template:Val... | ||
Gaussian integral | <math>\sqrt{\pi}</math> | Template:Val... | ||
Komornik–Loreti constant | <math>q</math> | Template:Val... | ||
Universal parabolic constant | <math>P_2</math> | Template:Val... | ||
Gelfond–Schneider constant | <math>2^{\sqrt{2}}</math> | Template:Val... | ||
Euler's number | <math>e</math> | Template:Val... | Raising e to the power of <math>i</math>Template:Pi will result in <math>-1</math>. | |
Pi | <math>
\pi</math> |
Template:Val... | Pi is a constant irrational number that is the result of dividing the circumference of a circle by its diameter. | |
Super square-root of 2 | <math display="inline">\sqrt{2}_s</math><ref>Template:Citation</ref> | Template:Val...<ref>{{#invoke:citation/CS1|citation | CitationClass=web
}}</ref> |
|
Liouville constant | <math display="inline">L</math> | Template:Val... | ||
Champernowne constant | <math display="inline">C_{10}</math> | Template:Val... | This constant contains every number string inside it, as its decimals are just every number in order. (1,2,3,etc.) | |
Prouhet–Thue–Morse constant | <math display="inline">\tau</math> | Template:Val... | ||
Omega constant | <math>\Omega</math> | Template:Val... | ||
Cahen's constant | <math display="inline">C
</math> |
Template:Val... | ||
Natural logarithm of 2 | ln 2 | Template:Val | ||
Lemniscate constant | <math display="inline">\varpi</math> | Template:Val... | The ratio of the perimeter of Bernoulli's lemniscate to its diameter. | |
Tau | <math>\tau=2\pi</math> | Template:Val... | The ratio of the circumference to a radius, and the number of radians in a complete circle;<ref>"The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 69</ref><ref>Sequence Template:OEIS2C.</ref> 2 <math>\times</math> Template:Pi |
Irrational but not known to be transcendentalEdit
Some numbers are known to be irrational numbers, but have not been proven to be transcendental. This differs from the algebraic numbers, which are known not to be transcendental. Template:Sticky header
Name | Decimal expansion | Proof of irrationality | Reference of unknown transcendentality |
---|---|---|---|
ζ(3), also known as Apéry's constant | Template:Val | <ref name="Apery-1979">See Template:Harvnb.</ref> | <ref>"The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 33</ref> |
Erdős–Borwein constant, E | Template:Val... | <ref>Template:Citation</ref><ref>Template:Citation</ref> | Template:Citation needed |
Copeland–Erdős constant | Template:Val... | Can be proven with Dirichlet's theorem on arithmetic progressions or Bertrand's postulate (Hardy and Wright, p. 113) or Ramare's theorem that every even integer is a sum of at most six primes. It also follows directly from its normality. | Template:Citation needed |
Prime constant, ρ | Template:Val... | Proof of the number's irrationality is given at prime constant. | Template:Citation needed |
Reciprocal Fibonacci constant, ψ | Template:Val... | <ref>André-Jeannin, Richard; 'Irrationalité de la somme des inverses de certaines suites récurrentes.'; Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, vol. 308, issue 19 (1989), pp. 539-541.</ref><ref>S. Kato, 'Irrationality of reciprocal sums of Fibonacci numbers', Master's thesis, Keio Univ. 1996</ref> | <ref>Duverney, Daniel, Keiji Nishioka, Kumiko Nishioka and Iekata Shiokawa; 'Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers';</ref> |
Real but not known to be irrational, nor transcendentalEdit
For some numbers, it is not known whether they are algebraic or transcendental. The following list includes real numbers that have not been proved to be irrational, nor transcendental. Template:Sticky header
Name and symbol | Decimal expansion | Notes | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Euler–Mascheroni constant, γ | Template:Val...<ref>{{#invoke:citation/CS1|citation | CitationClass=web
}}</ref> |
Believed to be transcendental but not proven to be so. However, it was shown that at least one of <math>\gamma</math> and the Euler-Gompertz constant <math>\delta</math> is transcendental.<ref name=":4">Template:Cite journal</ref><ref name=":5">Template:Cite journal</ref> It was also shown that all but at most one number in an infinite list containing <math>\frac{\gamma}{4}</math> have to be transcendental.<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> | |||||||
Euler–Gompertz constant, δ | citation | CitationClass=web
}}</ref> |
It was shown that at least one of the Euler-Mascheroni constant <math>\gamma</math> and the Euler-Gompertz constant <math>\delta</math> is transcendental.<ref name=":4" /><ref name=":5" /> | |||||||
Catalan's constant, G | Template:Val... | It is not known whether this number is irrational.<ref>Template:Citation</ref> | ||||||||
Khinchin's constant, K0 | Template:Val...<ref name=":1">{{#invoke:citation/CS1|citation | CitationClass=web
}}</ref> |
{{#if:|list|wrap}}|_template=cite web | _exclude=urlname, _debug, id | KhinchinsConstant.html}} | title = Khinchin's constant | author = Weisstein, Eric W. | website = MathWorld | access-date = | ref = Template:SfnRef
}}</ref> |
1st Feigenbaum constant, δ | 4.6692... | Both Feigenbaum constants are believed to be transcendental, although they have not been proven to be so.<ref name=Briggs>Template:Cite thesis</ref> | ||||||||
2nd Feigenbaum constant, α | 2.5029... | Both Feigenbaum constants are believed to be transcendental, although they have not been proven to be so.<ref name=Briggs/> | ||||||||
Glaisher–Kinkelin constant, A | Template:Val... | |||||||||
Backhouse's constant | Template:Val... | |||||||||
Fransén–Robinson constant, F | Template:Val... | |||||||||
Lévy's constant,β | 1.18656 91104 15625 45282... | |||||||||
Mills' constant, A | Template:Val... | It is not known whether this number is irrational.Template:Harv | ||||||||
Ramanujan–Soldner constant, μ | Template:Val... | |||||||||
Sierpiński's constant, K | Template:Val... | |||||||||
Totient summatory constant | Template:Val...<ref>Template:OEIS2C</ref> | |||||||||
Vardi's constant, E | Template:Val... | |||||||||
Somos' quadratic recurrence constant, σ | Template:Val... | |||||||||
Niven's constant, C | Template:Val... | |||||||||
Brun's constant, B2 | Template:Val... | The irrationality of this number would be a consequence of the truth of the infinitude of twin primes. | ||||||||
Landau's totient constant | Template:Val...<ref>Template:OEIS2C</ref> | |||||||||
Brun's constant for prime quadruplets, B4 | Template:Val... | |||||||||
Viswanath's constant | Template:Val... | |||||||||
Khinchin–Lévy constant | Template:Val...<ref>{{#invoke:citation/CS1|citation | CitationClass=web
}}</ref> |
This number represents the probability that three random numbers have no common factor greater than 1.<ref name="David Wells page 29">"The Penguin Dictionary of Curious and Interesting Numbers" by David Wells, page 29.</ref> | |||||||
Landau–Ramanujan constant | Template:Val... | |||||||||
C(1) | Template:Val... | |||||||||
Z(1) | Template:Val... | |||||||||
Heath-Brown–Moroz constant, C | Template:Val... | |||||||||
Kepler–Bouwkamp constant,K' | Template:Val... | |||||||||
MRB constant,S | Template:Val... | It is not known whether this number is irrational. | ||||||||
Meissel–Mertens constant, M | Template:Val... | |||||||||
Bernstein's constant, β | Template:Val... | |||||||||
Gauss–Kuzmin–Wirsing constant, λ1 | Template:Val...<ref>Template:Mathworld</ref> | |||||||||
Hafner–Sarnak–McCurley constant,σ | Template:Val... | |||||||||
Artin's constant,CArtin | Template:Val... | |||||||||
S(1) | Template:Val... | |||||||||
F(1) | Template:Val... | |||||||||
Stephens' constant | Template:Val...<ref>Template:OEIS2C</ref> | |||||||||
Golomb–Dickman constant, λ | Template:Val... | |||||||||
Twin prime constant, C2 | Template:Val... | |||||||||
Feller–Tornier constant | Template:Val...<ref>Template:OEIS2C</ref> | |||||||||
Laplace limit, ε | Template:Val...<ref>{{#invoke:citation/CS1|citation | CitationClass=web
}}</ref> |
||||||||
Embree–Trefethen constant | Template:Val... |
Numbers not known with high precisionEdit
Template:See also Some real numbers, including transcendental numbers, are not known with high precision.
- The constant in the Berry–Esseen Theorem: 0.4097 < C < 0.4748
- De Bruijn–Newman constant: 0 ≤ Λ ≤ 0.2
- Chaitin's constants Ω, which are transcendental and provably impossible to compute.
- Bloch's constant (also 2nd Landau's constant): 0.4332 < B < 0.4719
- 1st Landau's constant: 0.5 < L < 0.5433
- 3rd Landau's constant: 0.5 < A ≤ 0.7853
- Grothendieck constant: 1.67 < k < 1.79
- Romanov's constant in Romanov's theorem: 0.107648 < d < 0.49094093, Romanov conjectured that it is 0.434
Hypercomplex numbersEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} Hypercomplex number is a term for an element of a unital algebra over the field of real numbers. The complex numbers are often symbolised by a boldface Template:Math (or blackboard bold <math>\mathbb{\Complex}</math>, Unicode Template:Unichar), while the set of quaternions is denoted by a boldface Template:Math (or blackboard bold <math>\mathbb{H}</math>, Unicode Template:Unichar).
Algebraic complex numbersEdit
- Imaginary unit: <math display="inline">i=\sqrt{-1}</math>
- nth roots of unity: <math display="inline">\xi_{n}^{k}=\cos\bigl(2\pi\frac{k}{n}\bigr)+i\sin\bigl(2\pi\frac{k}{n}\bigr)</math>, while <math display="inline">0 \leq k \leq n-10</math>, GCD(k, n) = 1
Other hypercomplex numbersEdit
- The quaternions
- The octonions
- The sedenions
- The trigintaduonions
- The dual numbers (with an infinitesimal)
Transfinite numbersEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite.
- Aleph-null: ℵ0, the smallest infinite cardinal, and the cardinality of <math>\mathbb{N}</math>, the set of natural numbers
- Aleph-one: ℵ1, the cardinality of ω1, the set of all countable ordinal numbers
- Beth-one: <math>\beth_1</math> or <math>\mathfrak c</math>, the cardinality of the continuum 2ℵ0
- Omega: ω, the smallest infinite ordinal
Numbers representing physical quantitiesEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} Physical quantities that appear in the universe are often described using physical constants.
- Avogadro constant: Template:Physconst
- Electron mass: Template:Physconst
- Fine-structure constant: Template:Physconst
- Gravitational constant: Template:Physconst
- Molar mass constant: Template:Physconst
- Planck constant: Template:Physconst
- Rydberg constant: Template:Physconst
- Speed of light in vacuum: Template:Physconst
- Vacuum electric permittivity: Template:Physconst
Numbers representing geographical and astronomical distancesEdit
- [[Equator#Exact length|Template:Val]], the average equatorial radius of Earth in kilometers (following GRS 80 and WGS 84 standards).
- [[Equator#Exact length|Template:Val]], the length of the Equator in kilometers (following GRS 80 and WGS 84 standards).
- [[Lunar distance (astronomy)|Template:Val]], the semi-major axis of the orbit of the Moon, in kilometers, roughly the distance between the center of Earth and that of the Moon.
- [[Astronomical Unit|Template:Val]], the average distance between the Earth and the Sun or Astronomical Unit (AU), in meters.
- [[Light-year|Template:Val]], one light-year, the distance travelled by light in one Julian year, in meters.
- [[Parsec|Template:Val]], the distance of one parsec, another astronomical unit, in whole meters.
Numbers without specific valuesEdit
{{#invoke:Labelled list hatnote|labelledList|Main article|Main articles|Main page|Main pages}} Many languages have words expressing indefinite and fictitious numbers—inexact terms of indefinite size, used for comic effect, for exaggeration, as placeholder names, or when precision is unnecessary or undesirable. One technical term for such words is "non-numerical vague quantifier".<ref>"Bags of Talent, a Touch of Panic, and a Bit of Luck: The Case of Non-Numerical Vague Quantifiers" from Linguista Pragensia, Nov. 2, 2010 Template:Webarchive</ref> Such words designed to indicate large quantities can be called "indefinite hyperbolic numerals".<ref>Boston Globe, July 13, 2016: "The surprising history of indefinite hyperbolic numerals"</ref>
Named numbersEdit
- Hardy–Ramanujan number, 1729
- Kaprekar's constant, 6174
- Eddington number, ~1080
- Googol, 10100
- Shannon number
- Centillion, 10303
- Skewes's number
- Googolplex, 10(10100)
- Mega/Circle(2)
- Moser's number
- Graham's number
- TREE(3)
- SSCG(3)
- Rayo's number
See alsoEdit
Template:Portal Template:Div col
- Absolute infinite
- English numerals
- Floating-point arithmetic
- Fraction
- Integer sequence
- Interesting number paradox
- Large numbers
- List of mathematical constants
- List of prime numbers
- List of types of numbers
- Mathematical constant
- Metric prefix
- Names of large numbers
- Names of small numbers
- Negative number
- Numeral (linguistics)
- Numeral prefix
- Order of magnitude
- Orders of magnitude (numbers)
- Ordinal number
- The Penguin Dictionary of Curious and Interesting Numbers
- Perfect numbers
- Power of two
- Power of 10
- Surreal number
- Table of prime factors
ReferencesEdit
Further readingEdit
- Kingdom of Infinite Number: A Field Guide by Bryan Bunch, W.H. Freeman & Company, 2001. Template:Isbn
External linksEdit
- What's Special About This Number? A Zoology of Numbers: from 0 to 500
- Name of a Number
- See how to write big numbers
- Template:Webarchive
- Robert P. Munafo's Large Numbers page
- Different notations for big numbers – by Susan Stepney
- Names for Large Numbers, in How Many? A Dictionary of Units of Measurement by Russ Rowlett
- What's Special About This Number? (from 0 to 9999)