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

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.

Small natural numbers
0	1	2	3	4	5	6	7	8	9
10	11	12	13	14	15	16	17	18	19
20	21	22	23	24	25	26	27	28	29
30	31	32	33	34	35	36	37	38	39
40	41	42	43	44	45	46	47	48	49
50	51	52	53	54	55	56	57	58	59
60	61	62	63	64	65	66	67	68	69
70	71	72	73	74	75	76	77	78	79
80	81	82	83	84	85	86	87	88	89
90	91	92	93	94	95	96	97	98	99
100	101	102	103	104	105		107	108
									119
120

				144





		200	300	400	500	600	700	800	900
	1000					6000
10⁶	10⁹	10¹²					10¹⁵
larger numbers, along with 10¹⁰⁰ and 10^10¹⁰⁰

Classes of natural numbers change

Prime numbers change

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	97	101	103	107	109	113
127	131	137	139	149	151	157	163	167	173
179	181	191	193	197	199	211	223	227	229
233	239	241	251	257	263	269	271	277	281
283	293	307	311	313	317	331	337	347	349
353	359	367	373	379	383	389	397	401	409
419	421	431	433	439	443	449	457	461	463
467	479	487	491	499	503	509	521	523	541

Highly composite numbers change

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

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:

6
28
496
8128
33 550 336
8 589 869 056
137 438 691 328
2 305 843 008 139 952 128
2 658 455 991 569 831 744 654 692 615 953 842 176
191 561 942 608 236 107 294 793 378 084 303 638 130 997 321 548 169 216

Integers change

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

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.^[1]

Number	1000^m	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
1000	10³	Kilo	k
1000000	10⁶	Mega	M
1000000000	10⁹	Giga	G
1000000000000	10¹²	Tera	T
1000000000000000	10¹⁵	Peta	P
1000000000000000000	10¹⁸	Exa	E
1000000000000000000000	10²¹	Zetta	Z
1000000000000000000000000	10²⁴	Yotta	Y

Rational numbers change

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 $q$ .^[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 ( ${\frac {3}{25}}$ ), nine seventy-fifths ( ${\frac {9}{75}}$ ), etc.

Table of notable rational numbers
Decimal expansion	Fraction	Reason
1.0	${\bar {1}}$	${\bar {1}}$ is equal to 1, a notable real number.
1	${\bar {1}}$	${\bar {1}}$ is equal to 1, a notable real number.
0.5	${\bar {2}}$	${\bar {2}}$ is a popular number in math. For example, you can use ${\bar {2}}$ 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...	${\bar {6}}$	One sixth is seen in a lot of equations. For example, the solution to the Basel problem uses 1/6.

Irrational numbers change

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

Algebraic numbers change

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

Transcendental numbers change

Name	Symbol or Formula	Decimal expansion	Reason
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

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


Name and symbol	Decimal expansion	Notes
Euler–Mascheroni constant, γ	0.577215664901532860606512090082...^[3]	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

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

Algebraic complex numbers change

i, Imaginary unit: ${\textstyle i={\sqrt {-1}}}$

Transfinite numbers change

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

Physical Constants change

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

Named numbers change

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

↑ "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

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 $\zeta (2)$ et $\zeta (3)$ ", Astérisque, 61: 11–13.

Other Websites change

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)

[1] "What is Kilo, Mega, Giga, Tera, Peta, Exa, Zetta and All That?".

[Rosen-2] 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.

[3] "A001620 - OEIS". oeis.org. Retrieved 2020-10-14.

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