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.
Natural numbers[change | change source]
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.
|larger numbers, along with 10100 and 1010100|
Classes of natural numbers[change | change source]
Prime numbers[change | change source]
A prime number is a type of natural number. It only has two divisors: 1 and itself.
Highly composite numbers[change | change source]
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[change | change source]
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[change | change source]
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[change | change source]
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[change | change source]
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 (3/25), nine seventy-fifths (9/75), etc.
|1.0||1/1||1/1 is equal to 1, a notable real number.|
|0.5||1/2||1/2 is a popular number in math. For example, you can use 1/2 to find the area of a Triangle.|
|3.142 857...||22/7||22/7 is a number slightly above and is an approximation of .|
|0.166 666...||1/6||One sixth is seen in a lot of equations. For example, the solution to the Basel problem uses 1/6.|
Irrational numbers[change | change source]
Irrational numbers are numbers that cannot be written as a fraction. These are written as algebraic numbers or transcendental numbers.
Algebraic numbers[change | change source]
|Square root of two||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||1.561552812808830274910704927987|
|Phi, Golden ratio||1.618033988749894848204586834366||The golden ratio is a famous number used in both math and science.|
Transcendental numbers[change | change source]
|e, Euler's number||e||2.718281828459045235360287471352662497757247...||e is the base of a natural logarithm.|
|Pi||π||3.141592653589793238462643383279502884197169...||Pi is an irrational number that is the result of dividing the circumference of a circle by its diameter.|
Real numbers[change | change source]
The real numbers are a superset(or category) of numbers. They cover algebraic and transcendental numbers.
Real but not known if irrational or transcendental[change | change source]
|Name and symbol||Decimal expansion||Notes|
|Euler–Mascheroni constant, γ||0.577215664901532860606512090082...||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||0.660161815846869573927812110014...|
Hypercomplex numbers[change | change source]
A hypercomplex number is a word for an element of a unital algebra over the field of real numbers.
Algebraic complex numbers[change | change source]
- i, Imaginary unit:
Transfinite numbers[change | change source]
Transfinite numbers are numbers that are "infinite". They are larger than any finite number. They are, however, not absolutely infinite.
Physical Constants[change | change source]
Physical constants are constants that can be used in the universe to figure out information.
Named numbers[change | change source]
- 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
References[change | change source]
- ↑ "What is Kilo, Mega, Giga, Tera, Peta, Exa, Zetta and All That?".
- ↑ Rosen, Kenneth (2007). Discrete Mathematics and its Applications (6th ed.). New York, NY: McGraw-Hill. pp. 105, 158–160. ISBN 978-0-07-288008-3.
- ↑ "A001620 - OEIS". oeis.org. Retrieved 2020-10-14.
Bibliography[change | change source]
- 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 et ", Astérisque, 61: 11–13.
Further reading[change | change source]
- Kingdom of Infinite Number: A Field Guide by Bryan Bunch, W.H. Freeman & Company, 2001. ISBN 0-7167-4447-3
Other Websites[change | change source]
- 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)