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.

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. 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.

Classes of natural numbers

Prime numbers 

A prime number is a natural number which has only two divisors: 1 and itself.

Highly composite numbers 
A highly composite number is a natural number that 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 an integer that is 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.

Rational numbers 

A rational number is a number that can be written as a fraction with two integers. The numerator is written as  and 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.

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

Algebraic numbers

Transcendental numbers

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

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

Algebraic complex numbers 

 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, 10100
 Googolplex, 10(10100)
 Graham's number
 Skewes's number

References

Bibliography 

 
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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)

Numbers