List of numbers

This is a list of numbers. This list will always be not finished. This happens because there are an infinite amount of numbers. Only notable numbers will be added. Numbers can be added as long as they are popular in math, history or culture.

This means that numbers can only be notable if they are a big part of history. A number isn't notable if it is only related to another number. For example, the number (3,4) is a notable number
when it is a complex number (3+4i). When it is only (3,4), however, it's not notable. If a number is not important, that can also make the number important. This is called the interesting number paradox.

 Natural numbers 

Natural numbers are a type of integer. They can be used for counting. Natural numbers can also be used to find out about other number systems. The symbol  (or blackboard bold , Unicode ) is used to symbolize all of the natural numbers.. A negative number is not a natural number.

0 is argued on whether or not it is a natural number. In computer science and set theory, 0 is a natural number. In number theory, it is not. To fix this, people use the terms "non-negative integers". Non-negative integers includes the number 0. "Positive integers" does not.

Natural numbers can be used as cardinal numbers or ordinal numbers.
Table of small natural numbers012345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697989910010110210310410510610710810911011111211311411511611711811912012112212312412512612712812913013113213313413513613713813914014114214314414514614714814915015115215315415515615715815916016116216316416516616716816917017117217317417517617717817918018118218318418518618718818919019119219319419519619719819920020120220320420520620720820921021121221321421521621721821922022122222322422522622722822923023123223323423523623723823924024124224324424524624724824925025125225325425525625725825926026126226326426526626726826927027127227327427527627727827928028128228328428528628728828929029129229329429529629729829930030130230330430530630730830931031131231331431531631832332534135335936036336536938440042044049549650050151151255560070080090010002000300040005000600070008000900010,00020,00030,00040,00050,00060,00070,00080,00090,00010510610710810910101011larger numbers, including 10100 and 1010100

 Importance in math 
Natural numbers can be important in mathematics. This might be because it is part of a set. A number can also be important because it has a unique property.

 Importance in culture 
Many numbers are also important in culture. They can also be important for measurement.

 Classes of natural numbers 

 Prime numbers 

A prime number is a type of natural number. It only has two divisors: 1 and itself.

The first 100 prime numbers
   2  3  5  7 11 13 17 19 23 29
   31 37 41 43 47 53 59 61 67 71
   73 79 83 89 97101103107109113
  127131137139149151157163167173
  179181191193197199211223227229
  233239241251257263269271277281
  283293307311313317331337347349
  353359367373379383389397401409
  419421431433439443449457461463
  467479487491499503509521523541


 Highly composite numbers 
A highly composite number is a type of natural number. It has more divisors than any smaller natural number. They are used a lot 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 numbers 

A perfect number is a type of integer. It has the sum of its positive divisors (all divisors except itself).

The first 10 perfect numbers:

 Integers 

Integers are a set of numbers. They usually are in arithmetic and number theory. There are many subsets of integers. These can cover natural numbers, prime numbers, perfect numbers, etc.

Popular integers are −1 and 0.

 Orders of magnitude 
Integers can be written in orders of magnitude. This can be written as 10k, where k is an integer.  If k = 0, 1, 2, 3, then the powers of ten for them are 1, 10, 100 and 1000. This is used in scientific notation.

Each number has its own prefix. Each prefix has its own symbol. For example, kilo- may be added to the beginning of gram. This changes the meaning of gram to mean that the gram is 1000 times more than a gram: one kilogram is the same as 1000 grams.

Number1000mNameSymbol10-24Yoktoy10-21Zeptoz10-18Attoa10-15Femtof10-12Picop10-9Nanon10-6Microμ0.00110-3Millim0.0110-2Centic0.110-1Decid10101Decada100102Hectoh103Kilok106MegaM109GigaG1012TeraT1015PetaP1018ExaE1021ZettaZ1024YottaY

 Rational numbers 

A rational number is a number that can be written as a fraction with two integers. The numerator is written as . The denominator(which cannot be zero) is written as . Every integer is a rational number. This is because, in integers, 1 is always the denominator of a fraction.

Rational numbers can be written in infinitely many ways. For example, 0.12 can be written as three twenty-fifths (), nine seventy-fifths (), etc.

Table of notable rational numbersDecimal expansionFractionReason1.0 is equal to 1, a notable real number.10.5 is a popular number in math. For example, you can use  to find the area of a Triangle.3.142 857... is a number slightly above  and is an approximation of .0.166 666...One sixth is seen in a lot of equations. For example, the solution to the Basel problem uses 1/6.

 Irrational numbers 
Irrational numbers are numbers that cannot be written as a fraction. These are written as algebraic numbers or transcendental numbers.

 Algebraic numbers 

NameExpressionDecimal expansionReasonSquare root of twoThe Square root of 2(also called Pythagoras' constant) is a number used in math a lot. It can be used to find the ratio of diagonal to side length in a square.Triangular root of 2Phi, Golden ratioThe golden ratio is a famous number used in both math and science.

 Transcendental numbers 

NameSymbol
or

FormulaDecimal expansionReasone, Euler's numbere...e is the base of a natural logarithm.Pi...Pi is an irrational number that is the result of dividing the circumference of a circle by its diameter.

 Real numbers 
The real numbers are a superset(or category) of numbers. They cover algebraic and transcendental numbers.

 Real but not known if irrational or transcendental 

+Name and symbolDecimal expansionNotesEuler–Mascheroni constant, γ...The Euler–Mascheroni constant is used in limits and logarithms. It is thought to be transcendental but not proven to be so.Twin prime constant, C2...

 Hypercomplex numbers 
A hypercomplex number is a word for an element of a unital algebra over the field of real numbers.

 Algebraic complex numbers 

 i, Imaginary unit: 

 Transfinite numbers 

Transfinite numbers are numbers that are "infinite". They are larger than any finite number. They are, however, not absolutely infinite.

 Physical Constants 

Physical constants are constants that can be used in the universe to figure out information.

 Avogadro constant
 Gravitational constant
 Planck constant
 Rydberg constant 
 Speed of light in vacuum

 Named numbers 

 Googol, 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
 Googolplex, 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
 Graham's number, G
 Skewes's number, S

 References 

 Bibliography 


 .

 Further reading 

 Kingdom of Infinite Number: A Field Guide by Bryan Bunch, W.H. Freeman & Company, 2001. 

 Other websites 

 The Database of Number Correlations: 1 to 2000+ 
 What's Special About This Number? A Zoology of Numbers: from 0 to 500
 Name of a Number
 See how to write big numbers

 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)

Category:Numbers
Category:Mathematics lists