List of 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. A negative number is not a natural number.

0 is argued on whether or not it is a natural number. To fix this, people use the terms "non-negative integers", which cover 0 and "positive integers", which does not.

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.

A rational number is a number that can be written as a fraction with two integers. The numerator is written as ${\displaystyle p}$. The denominator(which cannot be zero) is written as ${\displaystyle q}$.[2] 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 (${\displaystyle {\frac {3}{25}}}$), nine seventy-fifths (${\displaystyle {\frac {9}{75}}}$), etc.

Table of notable rational numbers

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

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

Algebraic numbers

See the main article: Algebraic number

Name	Expression	Decimal expansion	Reason
Square root of two	${\displaystyle {\sqrt {2}}}$	1.414213562373095048801688724210	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	${\displaystyle {\frac {{\sqrt {17}}-1}{2}}}$	1.561552812808830274910704927987
Phi, Golden ratio	${\displaystyle \phi }$	1.618033988749894848204586834366	The golden ratio is a famous number used in both math and science.

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

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

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

• 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

• Finch, Steven R. (2003), "Anmol Kumar Singh", Mathematical Constants (Encyclopedia of Mathematics and its Applications, Series Number 94), Cambridge University Press, pp. 130–133, ISBN 0521818052
• Apéry, Roger (1979), "Irrationalité de ${\displaystyle \zeta (2)}$ et ${\displaystyle \zeta (3)}$", Astérisque, 61: 11–13.

• Kingdom of Infinite Number: A Field Guide by Bryan Bunch, W.H. Freeman & Company, 2001. ISBN 0-7167-4447-3

• The Database of Number Correlations: 1 to 2000+ Archived 2017-07-24 at the Wayback Machine
• What's Special About This Number? A Zoology of Numbers: from 0 to 500
• Name of a Number
• See how to write big numbers
• About big numbers at the Wayback Machine (archived 27 November 2010)
• 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? Archived 2018-02-23 at the Wayback Machine (from 0 to 9999)