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

Template:Main 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 Template:Math (or blackboard bold $\mathbb{N}$, Unicode Template:Unichar) 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.

Importance in math

Natural numbers can be important in mathematics. This might because it is part of a set. A number can also be important because it has a unique property.Template:Collapsible list

Importance in culture

Many numbers are also important in culture. They can also be important for measurement.Template:Collapsible listTemplate:Collapsible listTemplate:Collapsible list

Classes of natural numbers

Prime numbers

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

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 10^k, 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.

Number	1000m	Name	Symbol
0.0000000001	10-24	Yokto	y
0.000000001	10-21	Zepto	z
0.00000001	10-18	Atto	a
0.0000001	10-15	Femto	f
0.000001	10-12	Pico	p
0.00001	10-9	Nano	n
0.0001	10-6	Micro	μ
0.001	10-3	Mili	m
0.01	10-2	Centi	c
0.1	10-1	Deci	d
10	101	Deca	da
100	102	Hecto	h
Template:Gaps	103	Kilo	k
Template:Gaps	106	Mega	M
Template:Gaps	109	Giga	G
Template:Gaps	1012	Tera	T
Template:Gaps	1015	Peta	P
Template:Gaps	1018	Exa	E
Template:Gaps	1021	Zetta	Z
Template:Gaps	1024	Yotta	Y

Rational numbers

Template:Main A rational number is a number that can be written as a fraction with two integers. The numerator is written as $p$. The denominator(which cannot be zero) is written as $q$. 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 ($\frac{3}{25}$), nine seventy-fifths ($\frac{9}{75}$), etc.

Table of notable rational numbers

Decimal expansion	Fraction	Reason
1.0	$\overline{1}$	$\overline{1}$ is equal to 1, a notable real number.
1
0.5	$\overline{2}$	$\overline{2}$ is a popular number in math. For example, you can use $\overline{2}$ to find the area of a Triangle.
3.142 857...	$\frac{22}{7}$	$\frac{22}{7}$ is a number slightly above $\pi$ and is an approximation of $\pi$.
0.166 666...	$\overline{6}$	One sixth is seen in a lot of equations. For example, the solution to the Basel problem uses 1/6.

Irrational numbers

Template:MainIrrational numbers are numbers that cannot be written as a fraction. These are written as algebraic numbers or transcendental numbers.

Algebraic numbers

Name	Expression	Decimal expansion	Reason
Square root of two	$\sqrt{2}$	Template:Val	The 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 2	$\frac{\sqrt{17}-1}{2}$	Template:Val
Phi, Golden ratio	$\varphi$	Template:Val	The golden ratio is a famous number used in both math and science.

Transcendental numbers

Name	Symbol or Formula	Decimal expansion	Reason
e, Euler's number	e	Template:Val...	e is the base of a natural logarithm.
Pi	[[Pi|Template:Pi]]	Template:Val...	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 symbol	Decimal expansion	Notes
Euler–Mascheroni constant, γ	Template:Val...	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	Template:Val...

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: $i=\sqrt{-1}$

Transfinite numbers

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

Physical Constants

Template:Main 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, 10^{(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)}
• Graham's number, G
• Skewes's number, S

Bibliography

• Template:Citation
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Further reading

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

Other websites

• The Database of Number Correlations: 1 to 2000+ Template:Webarchive
• 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? Template:Webarchive (from 0 to 9999)