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@ -167,9 +167,9 @@ Of course there are countless other number sets, especially those induced by var
Worthy of mentioning is also [linear algebra](linear_algebra.md) which treats [vectors](vector.md) and [matrices](matrix.md) like elementary algebra treats numbers -- though vectors and matrices aren't usually seen as numbers, they may be seen as an extension of the concept.
**Numbers are [awesome](awesome.md)**, just ask any number theorist (or watch a numberphile video for that matter). Normal people perceive numbers just as boring, soulless quantities but the opposite is true for that who studies them with [love](love.md) -- the world of numbers is staggeringly beautiful, their study runs to depths without end, possibly as far as humans can ever hope to get a glimpse at the mechanisms of our [Universe](universe.md), and oftentimes once you pay a closer attention to a seemingly innocently looking detail, you reveal a breathtaking pattern and discover the [art](art.md) of nature. Each number has its own unique set of properties which give it a kind of "personality", different sets of numbers create species and "teams" of numbers. Numbers are intertwined in intricate ways, there are literally infinitely many patterns that are all related in weird ways -- normies think that mathematicians know basically everything about numbers, but in higher math it's the exact opposite, most things about number sequences are mysterious and mathematicians don't even have any clue about why they're so, many things are probably even [unknowable](knowability.md). Numbers are also self referencing which leads to new and new patterns appearing without end -- for example prime numbers are interesting numbers, but you may start counting them and a number that counts numbers is itself a number, you are getting new numbers just by looking at other numbers. The world of numbers is like a whole universe you can explore just in your head, anywhere you go, it's almost like the best, most free video [game](game.md) of all time, embedded right in this [Universe](universe.md), in [logic](logic.md) itself. Numbers are like animals, some are small, some big, some are hardly visible, trying to hide, some can't be overlooked -- they inhabit various areas and interact with each other, just exploring this can make you quite happy. { Pokemon-like game with numbers when? ~drummyfish }
**Numbers are [awesome](awesome.md)**, just ask any number theorist (or watch a numberphile video for that matter). Normal people perceive numbers just as boring, soulless quantities but the opposite is true for that who studies them with [love](love.md) -- the world of numbers is without a doubt staggeringly beautiful, their study runs to depths without end, possibly as far as humans can ever hope to get a glimpse of the mechanisms behind the curtains of our [Universe](universe.md), and oftentimes once you pay a closer attention to a seemingly innocently looking detail, you reveal a breathtaking pattern and discover the [art](art.md) of nature. Each number has its own unique set of properties which give it a kind of "personality", different sets of numbers create species and "teams" of numbers. Numbers are intertwined in intricate ways, there are literally infinitely many patterns that are all related in weird ways -- normies think that mathematicians know basically everything about numbers, but in higher math it's the exact opposite, most things about number sequences are mysterious and mathematicians don't even have any clue about why they're so, many things are probably even [unknowable](knowability.md). Numbers are also self referencing which leads to new and new patterns appearing without end -- for example prime numbers are interesting numbers, but you may start counting them and a number that counts numbers is itself a number, you are getting new numbers just by looking at other numbers. The world of numbers is like a whole universe you can explore just in your head, anywhere you go, it's almost like the best, most free video [game](game.md) of all time, embedded right in this [Universe](universe.md), in [logic](logic.md) itself. Numbers are like animals, some are small, some big, some are hardly visible, trying to hide, some can't be overlooked -- they inhabit various areas and interact with each other, just exploring this can make you quite happy. { Pokemon-like game with numbers when? ~drummyfish }
There is a famous [encyclopedia](encyclopedia.md) of integer sequences at https://oeis.org/, made by number theorists -- it's quite [minimalist](minimalism.md), now also [free licensed](free_culture.md) (used to be [proprietary](proprietary.md), they seem to enjoy license hopping). At the moment it contains more than 370000 sequences; by browsing it you can get a glimpse of how deep the study of numbers goes. These people are also [funny](fun.md), they give numbers entertaining names like *happy numbers* (adding its squared digits eventually gives 1), *polite numbers*, *friendly numbers*, *cake numbers*, *lucky numbers* or *weird numbers*.
There is a famous [encyclopedia](encyclopedia.md) of integer sequences at https://oeis.org/, made by number theorists -- it's quite [minimalist](minimalism.md), now also [free licensed](free_culture.md) (used to be [proprietary](proprietary.md), they seem to enjoy license hopping). At the moment it contains more than 370000 sequences; by browsing it you can get a glimpse of how deep the study of numbers goes. These people are also somewhat [funny](fun.md), they give numbers entertaining names like *happy numbers* (adding its squared digits eventually gives 1), *polite numbers*, *friendly numbers*, *cake numbers*, *lucky numbers* or *weird numbers*.
**Some numbers cannot be computed**, i.e. there exist [noncomputable](computability.md) numbers. This follows from the existence of noncomputable functions (such as that representing the [halting problem](halting_problem.md)). For example let's say we have a real number *x*, written in [binary](binary.md) as *0. d0 d1 d2 d3 ...*, where *dn* is *n*th digit (1 or 0) after the radix point. We can define the number so that *dn* is 1 if and only if a [Turing machine](turing_machine.md) represented by number *n* halts. Number *x* is noncomputable because to compute the digits to any arbitrary precision would require being able to solve the unsolvable halting problem.
@ -179,7 +179,7 @@ TODO: what is the best number? maybe top 10? would 10 be in top 10? what's the f
## Numbers In Programming/Computers
While mathematicians work mostly with infinite number sets and all kind of "weird" hypothetical numbers like hyperreals and transcendentals, [programmers](programming.md) still mostly work with "normal" numbers pertaining to practical applications, and have to limit themselves to finite number sets because, of course, computers have limited memory and can only store limited number of numeric values -- computers typically work with [modulo](mod.md) arithmetic with some high power of two modulo, e.g. 2^32 or 2^64, which is a [good enough](good_enough.md) approximation of an infinite number set. Mathematicians are as precise with numbers as possible as they're interested in structures and patterns that numbers form, programmers just want to use numbers to solve problems, so they mostly use [approximations](approximation.md) where they can -- for example programmers normally approximate [real numbers](real_number.md) with [floating point](float.md) numbers that are really just a subset of rational numbers. This isn't really a problem though, computers can comfortably work with numbers large and precise enough for solving any practical problem -- a slight annoyance is that one has to be careful about such things as [underflows](underflow.md) and [overflows](overflow.md) (i.e. a value wrapping around from lowest to highest value and vice versa), limited and sometimes non-uniform precision resulting in [error](error.md) accumulation, unlinearization of linear systems and so on. Programmers also don't care about strictly respecting some properties that certain number sets must mathematically have, for example integers along with addition are mathematically a [group](group.md), however signed integers in [two's complement](twos_complement.md) aren't a group because the lowest value doesn't have an inverse element (e.g. on 8 bits the lowest value is -128 and highest 127, the lowest value is missing its partner). Programmers also allow "special" values to be parts of their number sets, especially e.g. with the common IEEE [floating point](float.md) types we see values like plus/minus [infinity](infinity.md), [negative zero](negative_zero.md) or [NaN](nan.md) ("not a number") which also break some mathematical properties and creates situations like having a number that says it's not a number, but again this really doesn't play much of a role in practical problems. Numbers in computers are represented in [binary](binary.md) and programmers themselves often prefer to write numbers in binary, hexadecimal or octal representation -- they also often meet powers of two rather than powers of ten or primes or other similar limits (for example the data type limits are typically limited by some power of two). There also comes up the question of specific number encoding, for example direct representation, sign-magnitude, [two's complement](twos_complement.md), [endianness](byte_sex.md) and so on. Famously programmers start counting from 0 (they go as far as using the term "zeroth") while mathematicians rather tend to start at 1. Just as mathematicians have different sets of numbers, programmers have an analogy in numeric [data types](data_type.md) -- a data type defines a set of values and operations that can be performed with them. The following are some of the common data types and representations of numbers in computers:
While mathematicians work mostly with infinite number sets and all kinds of "weird" hypothetical numbers like hyperreals and transcendentals, [programmers](programming.md) still typically deal with "normal" numbers pertaining to practical applications, and have to limit themselves to finite number sets because, of course, computers have limited memory and can only store limited number of numeric values -- computers typically work with [modulo](mod.md) arithmetic with some high power of two, e.g. 2^32 or 2^64, which is a [good enough](good_enough.md) [approximation](approximation.md) of an infinite number set. Mathematicians are as precise with numbers as possible as they're interested in structures and patterns that numbers form, programmers just want to use numbers to solve problems, so they mostly use [approximations](approximation.md) where they can -- for example programmers normally approximate [real numbers](real_number.md) with [floating point](float.md) numbers that are really just a subset of rational numbers. This isn't really a problem though, computers can comfortably work with numbers large and precise enough for solving any practical problem -- a slight annoyance is that one has to be careful about such things as [underflows](underflow.md) and [overflows](overflow.md) (i.e. a value wrapping around from lowest to highest value and vice versa), limited and sometimes non-uniform precision resulting in [error](error.md) accumulation, unlinearization of linear systems and so on. Programmers also don't care about strictly respecting some properties that certain number sets must mathematically have, for example integers along with addition are mathematically a [group](group.md), however signed integers in [two's complement](twos_complement.md) aren't a group because the lowest value doesn't have an inverse element (e.g. on 8 bits the lowest value is -128 and highest 127, the lowest value is missing its partner). Programmers also allow "special" values to be parts of their number sets, especially e.g. with the common IEEE [floating point](float.md) types we see values like plus/minus [infinity](infinity.md), [negative zero](negative_zero.md) or [NaN](nan.md) ("not a number") which also break some mathematical properties and creates situations like having a number that says it's not a number, but again this really doesn't play much of a role in practical problems. Numbers in computers are represented in [binary](binary.md) and programmers themselves often prefer to write numbers in binary, hexadecimal or octal representation -- they also often meet powers of two rather than powers of ten or primes or other similar limits (for example the data type limits are typically limited by some power of two). There also comes up the question of specific number encoding, for example direct representation, sign-magnitude, [two's complement](twos_complement.md), [endianness](byte_sex.md) and so on. Famously programmers start counting from 0 (they go as far as using the term "zeroth") while mathematicians rather tend to start at 1. Just as mathematicians have different sets of numbers, programmers have an analogy in numeric [data types](data_type.md) -- a data type defines a set of values and operations that can be performed with them. The following are some of the common data types and representations of numbers in computers:
- **numeric**: Anything considered a number. In very high level languages there may be just one generic "number" type that can store any kind of number, automatically choosing best representation for it etc.
- **[unsigned](unsigned.md)**: Don't allow negative values -- this is sufficient in many cases, simpler to implement and can offer higher range in the positive direction.
@ -203,97 +203,178 @@ However some programming languages, such as [Lisp](lisp.md), sometimes treat num
## Notable Numbers
Here is a table of some numbers worthy of mention, mostly relevant in math and programming but also some famous ones from [physics](physics.md) and popular [culture](culture.md) (note: the order is roughly from lower numbers to higher ones, however not all of these numbers can be compared easily or at all, so the ordering isn't strictly correct).
Here is a table of some numbers and "number like objects" worthy of mention, mostly relevant in math and programming but also some famous ones from [physics](physics.md) and popular [culture](culture.md) (note: the order is roughly from lower numbers to higher ones, however not all of these numbers can be compared easily or at all, so the ordering isn't strictly correct).
| number | value | equal to | notes |
| ----------------------------------- | ------------------- | ---------------------------------------- | ------------------------------------------------------- |
| minus [infinity](infinity.md) | | | not always considered a number, smallest possible value |
| minus/negative one | -1 | i^2, j^2, k^2 | |
| "[negative zero](negative_zero.md)" | "-0" | zero | non-mathematical, sometimes used in programming |
| [zero](zero.md) | 0 | negative zero, e^(i * pi) + 1 | "nothing" |
| epsilon | | 1 / omega | infinitesimal, "infinitely small" non-zero |
| |4.940656... * 10^-324| | smallest number storable in IEEE-754 64 binary float |
| |1.401298... * 10^-45 | | smallest number storable in IEEE-754 32 binary float |
| |1.616255... * 10^-35 | | Planck length in meters, smallest "length" in Universe |
| one eight | 0.125 | 2^-3 | |
| one fourth | 0.25 | 2^-2 | |
| one third | 0.333333... | ...1313132 (5-adic) | |
| one half | 0.5 | 2^-1 | |
| [one](one.md) | 1 | 2^0, 0!, 0.999... | NOT a prime |
| [square root](sqrt.md) of two | 1.414213... | 2^(1/2) | irrational, diagonal of unit square, important in geom. |
| supergolden ratio | 1.465571... | solve(x^3 - x^2 - 1 = 0) | similar to golden ratio, bit more difficult to compute |
|phi ([golden ratio](golden_ratio.md))| 1.618033... | (1 + sqrt(5)) / 2, solve(x^2 - x - 1 = 0)| irrational, visually pleasant ratio, divine proportion |
| [two](two.md) | 2 | 2^1, 0b000010 | (only even) prime |
| [silver ratio](silver_ratio.md) | 2.414213... | 1 + sqrt(2), solve(x^2 - 2 * x - 1 = 0) | similar to golden ratio |
| [e](e.md) (Euler's number) | 2.718281... | | base of natural [logarithm](log.md) |
| [three](three.md) | 3 | 2^2 - 1 | prime, max. unsigned number with 2 bits |
| [pi](pi.md) | 3.141592... | | circle circumference to its diameter, irrational |
| [four](four.md) | 4 | 2^2, 0b000100 |first composite number, min. needed to color planar graph|
| [five](five.md) | 5 | | (twin) prime, number of platonic solids |
| [six](six.md) | 6 | 3!, 1 * 2 * 3, 1 + 2 + 3 | highly composite number, perfect number |
| [tau](tau.md) | 6.283185... | 2 * pi | radians in full circle, defined mostly for convenience |
| [thrembo](thrembo.md) | ??? | | the hidden number |
| [seven](seven.md) | 7 | 2^3 - 1 |(twin) prime, days in week, max. unsigned n. with 3 bits |
| [eight](eight.md) | 8 | 2^3, 0b001000 | |
| [nine](nine.md) | 9 | | |
| [ten](ten.md) | 10 | 10^1, 1 + 2 + 3 + 4 | your IQ? :D |
| twelve, dozen | 12 | 2 * 2 * 3 | highly composite number |
| fifteen | 15 | 2^4 - 1, 0b1111, 0x0f, 1 + 2 + 3 + 4 + 5 | maximum unsigned number storable with 4 bits |
| [sixteen](sixteen.md) | 16 | 2^4, 2^2^2, 0b010000 | |
| twenty four | 24 | 2 * 2 * 2 * 3, 4! | highly composite number |
| thirty one | 31 | 2^5 - 1 |max. unsigned number storable with 5 bits, Mersenne prime|
| [thirty two](thirty_two.md) | 32 | 2^5, 0b100000 | |
| thirty six | 36 | 2 * 2 * 3 * 3 | highly composite number |
| thirty seven | 37 | | most commonly chosen 1 to 100 "random" number |
| [fourty two](42.md) | 42 | | cringe number, answer to some stuff |
| fourty eight | 48 | 2^5 + 2^4, 2 * 2 * 2 * 2 * 3 | highly composite number |
| sixty three | 63 | 2^6 - 1 | maximum unsigned number storable with 6 bits |
| [sixty four](sixty_four.md) | 64 | 2^6 | |
| [sixty nine](69.md) | 69 | | sexual position |
| ninety six | 96 | 2^5 + 2^6 | alternative sexual position |
| one hundred | 100 | 10^2 | |
| one hundred twenty one | 121 | 11^2 | |
| one hundred twenty seven | 127 | 2^7 - 1 | maximum value of signed byte, Mersenne prime |
| one hundred twenty eight | 128 | 2^7 | |
| one hundred fourty four | 144 | 12^2 | |
| one hundred sixty eight | 168 | 24 * 7 | hours in week |
| two hundred fifty five | 255 | 2^8 - 1, 0b11111111, 0xff | maximum value of unsigned [byte](byte.md) |
| two hundred fifty six | 256 | 2^8, 16^2, ((2^2)^2)^2 | number of values that can be stored in one byte |
| three hundred sixty | 360 | 2 * 2 * 2 * 3 * 3 * 5 | highly composite number, degrees in full circle |
| four hundred twenty | 420 | | stoner shit (they smoke it at 4:20), divisible by 1 to 7|
| five hundred twelve | 512 | 2^9 | |
| six hundred and sixty six | 666 | | number of the beast |
| one thousand | 1000 | 10^3 | |
| one thousand twenty four | 1024 | 2^10 | |
| two thousand fourty eight | 2048 | 2^11 | |
| four thousand ninety six | 4096 | 2^12 | |
| ten thousand | 10000 | 10^4, 100^2 | |
| ... (enough lol) | 65535 | 2^16 - 1 | maximum unsigned number storable with 16 bits |
| | 65536 | 2^16, 256^2, 2^(2^(2^2)) | number of values storable with 16 bits |
| | 80085 | | looks like BOOBS |
| hundred thousand | 100000 | 10^5 | |
| one [million](million.md) | 1000000 | 10^6 | |
| one [billion](billion.md) | 1000000000 | 10^9 | |
| | 3735928559 | 0xdeadbeef | one of famous hexadeciaml constants, spells out DEADBEEF|
| | 4294967295 | 2^32 - 1, 0xffffffff | maximum unsigned number storable with 32 bits |
| | 4294967296 | 2^32 | number of values storable with 32 bits |
| one trillion | 1000000000000 | 10^12 | |
| |18446744073709551615 | 2^64 - 1 | maximum unsigned number storable with 64 bits |
| |18446744073709551616 | 2^64 | number of values storable with 64 bits |
| | 3.402823... * 10^38 | | largest number storable in IEEE-754 32 binary float |
| | 10^80 | | approx. number of atoms in observable universe |
| [googol](googol.md) | 10^100 | | often used big number |
| [asankhyeya](asankhyeya.md) | 10^140 | | religious number, often used in [Buddhism](buddhism.md) |
| | 4.65... * 10^185 | | approx. number of Planck volumes in observable universe |
| |1.797693... * 10^308 | | largest number storable in IEEE-754 64 binary float |
| [googolplex](googolplex.md) | 10^(10^100) | 10^googol | another large number, number of genders in 21st century |
| [Graham's number](grahams_number.md)| | g64 | extremely, unimaginably large number, > googolplex |
| TREE(3) | unknown | | yet even larger number, > Graham's number |
| [infinity](infinity.md) | | | not always considered a number, largest possible value |
| [aleph](aleph.md) zero | | beth zero, cardinality(N) | infinite cardinal number, "size" of the set of nat. num.|
| [i](i.md) (imaginary unit) | | j * k | part of complex numbers and quaternions |
| [j](j.md) | | k * i | one of quaternion units |
| [k](k.md) | | i * j | one of quaternion units |
| number | value | equal to, AKA | notes |
| ----------------------------------- | -------------------- | ---------------------------------------- | ------------------------------------------------------- |
| not a number (NaN, undefined, ...) | none | 1/0, 0^0, tan(pi/2) | error value |
| minus [infinity](infinity.md) | | | not always considered a number, smallest possible value |
| |-1.797693... * 10^308 | | smallest number storable in IEEE-754 64 bit float |
| | -3.402823... * 10^38 | | smallest number storable in IEEE-754 32 bit float |
| | -9223372036854776000 | -1 * 2^64 / 2 | minimum two's complement signed 64 bit number |
| | -2147483648 | -1 * 2^32 / 2 | minimum two's complement signed 32 bit number |
| minus thirty two thousand seven ... | -32768 | -1 * 2^16 / 2 | minimum two's complement signed 16 bit number |
| minus one hundred twenty eight | -128 | -1 * 2^7 | minimum value of signed byte (two's complement) |
| minus/negative one | -1 | i^2, j^2, k^2 | |
| "[negative zero](negative_zero.md)" | "-0" | 0 | non-mathematical, sometimes used in programming |
| [zero](zero.md) | 0 | "-0", e^(i * pi) + 1, lim x->inf 1/x | "nothing", additive identity |
| epsilon | | 1 / omega | infinitesimal, "infinitely small" non-zero |
| |4.940656... * 10^-324 | | smallest pos. number storable in IEEE-754 64 bit float |
| | 1.401298... * 10^-45 | | smallest pos. number storable in IEEE-754 32 bit float |
| | 1.616255... * 10^-35 | | Planck length in meters, smallest "length" in Universe |
| one eight | 0.125 | 2^-3 | |
| one fourth | 0.25 | 2^-2 | |
| one third | 0.333333... | ...1313132 (5-adic) | |
| one half | 0.5 | 2^-1 | |
| one over square root of two | 0.707106... | 1/sqrt(2), sin(pi/4), cos(pi/4), 2^(-1/2)| |
| [one](one.md) | 1 |2^0, 0!, 0.999..., sqrt(1), I, 0b1, cos(0)| NOT a prime, unit, multiplicative identity |
| [square root](sqrt.md) of two | 1.414213... | sqrt(2), 2^(1/2) | irrational, diagonal of unit square, important in geom. |
| supergolden ratio | 1.465571... | solve(x^3 - x^2 - 1 = 0) | similar to golden ratio, bit more difficult to compute |
|phi ([golden ratio](golden_ratio.md))| 1.618033... | (1 + sqrt(5)) / 2, solve(x^2 - x - 1 = 0)| irrational, visually pleasant ratio, divine proportion |
| square root of three | 1.732050... | sqrt(3), 3^(1/2) | irrational |
| [two](two.md) | 2 | 2^1, 2!, 2!!, 0b000010, II, 0b10 | (only even) prime, base of [binary](binary.md) system |
| [silver ratio](silver_ratio.md) | 2.414213... | 1 + sqrt(2), solve(x^2 - 2 * x - 1 = 0) | similar to golden ratio |
| [e](e.md) (Euler's number) | 2.718281... | | base of natural [logarithm](log.md) |
| [three](three.md) | 3 | 2^2 - 1, III, Ob11 | prime, max. number on 2 bits, regular plane tilings |
| [pi](pi.md) | 3.141592... | 2 * asin(1) | circle circumference to its diameter, irrational |
| [four](four.md) | 4 | 2^2, 0b000100, IV, 0b100 |first composite number, min. needed to color planar graph|
| [five](five.md) | 5 | 3^2 - 2^2, V, 0b101 | (twin) prime, number of platonic solids |
| [six](six.md) | 6 | 3!, 1 * 2 * 3, 1 + 2 + 3, VI, 0b110 | highly composite number, perfect number |
| [tau](tau.md) | 6.283185... | 2 * pi | radians in full circle, defined mostly for convenience |
| [thrembo](thrembo.md) | ??? | | the hidden number |
| [seven](seven.md) | 7 | 2^3 - 1, VII, 0b111 |(twin) prime, days in week, max. unsigned n. with 3 bits |
| [eight](eight.md) | 8 | 2^3, 0b001000, VIII, 0b1000 | base of [octal](oct.md) system |
| [nine](nine.md) | 9 | 3^3, 1^3 + 2^3, sqrt(81), IX, 0b1001 | |
| [ten](ten.md) | 10 | 10^1, 1 + 2 + 3 + 4, X, 0b1010 | your IQ? :D base of our decimal system |
| eleven | 11 | XI, 0b1011 | palindromic prime |
| twelve, dozen | 12 | 2 * 2 * 3, XII, 0b1100 | highly composite number |
| fifteen | 15 | 2^4 - 1, 0b1111, 0x0f, 1 + 2 + 3 + 4 + 5 | maximum unsigned number storable with 4 bits |
| [sixteen](sixteen.md) | 16 | 2^4, 2^2^2, 0b010000, 0x10, XVI | base of [hexadecimal](hex.md) system |
| twenty one | 21 | BB(3), XXI | maximum number of 1s produced by 3 state Turing Machine |
| twenty four | 24 | 2 * 2 * 2 * 3, 4!, XXIV |highly composite number, possible ways to order 4 objects|
| twenty five | 25 | 5^2, sqrt(625), XXV | |
| thirty one | 31 | 2^5 - 1, 0b11111, 0x1f, XXXI |max. unsigned number storable with 5 bits, Mersenne prime|
| [thirty two](thirty_two.md) | 32 | 2^5, 0b100000, 0x20, XXXII | number of possible values storable with 5 bits |
| thirty three | 33 | 1! + 2! + 3! + 4!, XXXIII | |
| thirty six | 36 | 2 * 2 * 3 * 3, XXXVI | highly composite number |
| thirty seven | 37 | XXXVII | most commonly chosen 1 to 100 "random" number |
| [forty two](42.md) | 42 | XLII | cringe number, answer to some stuff |
| forty eight | 48 |2^5 + 2^4, 2 * 2 * 2 * 2 * 3, XLVIII, 0x30| highly composite number |
| forty nine | 49 | 7^2 | |
| fifty | 50 | L | |
| fifty five | 55 | 1 + 2 + ... + 10, LV | sum of numbers up to 10 |
| sixty three | 63 | 2^6 - 1, LXIII | maximum unsigned number storable with 6 bits |
| [sixty four](sixty_four.md) | 64 | 2^6, LXIV, 0x40 | number of squares on a chess board |
| [sixty nine](69.md) | 69 | LXIX | sexual position |
| eighty one | 81 | 3^4, 9*9, XXCI | |
| ninety six | 96 | 2^5 + 2^6, 5! - 4!, 0x60 | alternative sexual position |
| one hundred | 100 | 10^2, 0x64, C | |
| one hundred seven | 107 | BB(4) | maximum number of 1s produced by 4 state Turing machine |
| one hundred twenty | 120 | 5!, C(10,3), CXX | possible ways to order 5 objects |
| one hundred twenty one | 121 | 11^2, CXXI | [palindromic](palindrome.md) |
| one hundred twenty five | 125 | 5^3, CXXV | |
| one hundred twenty seven | 127 | 2^7 - 1, 0x7f, 0b01111111, CXXVII | maximum value of signed byte, Mersenne prime |
| one hundred twenty eight | 128 | 2^7, 0x80, 0b10000000, CXXVIII | |
| one hundred forty four | 144 | 12^2, CXLIV | |
| one hundred sixty eight | 168 | 24 * 7, CLXVIII | hours in week |
| two hundred forty three | 243 | 3^5, CCXLIII | |
| two hundred fifty five | 255 | 2^8 - 1, 0xff, 0b11111111, CCLV | maximum value of unsigned [byte](byte.md) |
| two hundred fifty six | 256 | 2^8, 16^2, 0x100, ((2^2)^2)^2, CCLVI | number of values that can be stored in one byte |
| three hundred forty three | 343 | 7^3, CCCXLIII | |
| three hundred sixty | 360 | 2 * 2 * 2 * 3 * 3 * 5, CCCLX | highly composite number, degrees in full circle |
| three hundred sixty five | 365 | CCCLXV | days in a year |
| four hundred twenty | 420 | CDXX | stoner shit (they smoke it at 4:20), divisible by 1 to 7|
| five hundred eleven | 511 | 2^9 - 1, DXI | largest number storable with 9 bits |
| five hundred twelve | 512 | 2^9, 2^(3^2), DXII | number of values storable with 9 bits |
| six hundred twenty five | 625 | 25^2, 5^4, DCXXV | |
| six hundred and sixty six | 666 | DCLXVI | number of the beast, palindromic |
| seven hundred twenty | 720 | 6!, 3!!, DCCXX | possible ways to order 6 objects |
| seven hundred twenty nine | 729 | 3^6, (3^2)^3, DCCXXIX | |
| one thousand | 1000 | 10^3, M, 0x3e8 | |
| one thousand twenty three | 1023 | 2^10 - 1, 0x3ff, MXXIII | largest number storable with 10 bits |
| one thousand twenty four | 1024 | 2^10, 0x400, MXXIV | number of values storable with 10 bits |
| two thousand forty eight | 2048 | 2^11, 0x800, MMXLVIII | number of values storable with 11 bits |
|two thousand one hundred eighty seven| 2187 | 3^7, MMCXXCVII | |
| two thousand four hundred one | 2401 | 7^4, MMCDI | |
| three thousand one hundred ... | 3125 | 5^5, MMMCXXV | |
| three thousand nine hundred ... | 3999 | MMMCMXCIX | largest number that can be written with Roman numerals |
| four thousand ninety six | 4096 | 2^12, 2^(3^4), 0x1000 | number of values storable with 12 bits |
| five thousand forty | 5040 | 7!, 1 * 2 * ... * 7 | possible ways to order 7 objects |
| five thousand fifty | 5050 | 1 + 2 + ... + 100 | sum of numbers up to 100 |
| six thousand five hundred sixty one | 6561 | 3^8, 3^(2^3) | |
| ten thousand | 10000 | 10^4, 100^2 | |
| fifteen thousand six hundred ... | 15625 | 5^6 | |
| sixteen thousand eight hundred ... | 16807 | 7^5 | |
| nineteen thousand six hundred ... | 19683 | 3^9, 3^(3^3) | |
|thirty two thousand seven hundred ...| 32767 | 2^16 / 2 - 1, 0x7fff | maximum two's complement signed 16 bit number |
| forty thousand three hundred twenty | 40320 | 8!, 1 * 2 * ... * 8 | possible ways to order 8 objects |
| ... (enough lol) | 59049 | 3^10 | |
| | 65504 | | largest number storable in IEEE-754 16 bit float |
| | 65535 | 2^16 - 1, 0xffff | maximum unsigned number storable with 16 bits |
| | 65536 | 2^16, 256^2, 0x10000, 2^(2^(2^2)) | number of values storable with 16 bits |
| | 72078 | | number of possible chess positions after 4 half moves |
| | 80085 | | looks like BOOBS |
| | 86400 | 60 * 60 * 24 | seconds in a day |
| hundred thousand | 100000 | 10^5 | |
| | 362880 | 9!, 1 * 2 * ... * 9 | possible ways to order 9 objects |
| | 500500 | 1 + 2 + ... + 1000 | sum of numbers up to 1000 |
| one [million](million.md) | 1000000 | 10^6 | |
| | 3197281 | | number of possible chess games after 4 half moves |
| | 3628800 | 10!, 1 * 2 * ... * 10 | possible ways to order 10 objects |
| | 16777216 | 2^24, 16^6, 0xffffff | number of distinct 24 bit values (e.g. RGB24 colors) |
| | 43046721 | 3^16 | |
| | 47176870 | BB(5) | maximum number of 1s produced by 5 state Turing machine |
| | 31556926 | | seconds in a year |
| | 39916800 | 11!, 1 * 2 * ... * 11 | possible ways to order 11 objects |
| | 479001600 | 12!, 1 * 2 * ... * 12 | possible ways to order 12 objects |
| one [billion](billion.md) | 1000000000 | 10^9, milliard | |
| | 2147483647 | 2^32 / 2 - 1 | maximum two's complement signed 32 bit number |
| | 3735928559 | 0xdeadbeef | one of famous hexadeciaml constants, spells out DEADBEEF|
| | 4294967295 | 2^32 - 1, 0xffffffff | maximum unsigned number storable with 32 bits |
| | 4294967296 | 2^32, ((((2^2)^2)^2)^2)^2, 0x100000000 | number of values storable with 32 bits |
| | 6227020800 | 13!, 1 * 2 * ... * 13 | possible ways to order 13 objects |
| | 87178291200 | 14!, 1 * 2 * ... * 14 | possible ways to order 14 objects |
| | 500000500000 | 1 + 2 + ... + 1000000 | sum of numbers up to 1000000 |
| one trillion | 1000000000000 | 10^12, billion (LS) | |
| | 1307674368000 | 15! | possible ways to order 15 objects |
| | 20922789888000 | 16! | possible ways to order 16 objects |
| thirty trillion | 30000000000000 | | approximate number of cells in human body |
| | 355687428096000 | 17! | possible ways to order 17 objects |
| bazillion | ??? | | used to just express a very large value |
| quadrillion | 1000000000000000 | 10^15 | |
| | 6402373705728000 | 18! | possible ways to order 18 objects |
| | 121645100408832000 | 19! | possible ways to order 19 objects |
| quintillion | 1000000000000000000 | 10^18 | |
| | 2432902008176640000 | 20! | possible ways to order 20 objects |
| | 9223372036854776000 | 2^64 / 2 - 1 | maximum two's complement signed 64 bit number |
| | 43252003274489856000 | | number of possible Rubik's cube configurations |
| | 18446744073709551615 | 2^64 - 1, 0xffffffffffffffff | maximum unsigned number storable with 64 bits |
| | 18446744073709551616 | 2^64 | number of values storable with 64 bits |
| |2015099950053364471960| | number of possible chess games after 15 half moves |
| |6670903752021072936960| | possible valid filled [sudoku](sudoku.md) grids |
| | 1.267650... * 10^30 | 2^100 | number of values storable with 100 bits |
| | 3.402823... * 10^38 | (2 - 2^(-23)) * 2^127 | largest number storable in IEEE-754 32 bit float |
| | 3.402823... * 10^38 | 2^128 | number of values storable with 128 bits |
| | 1.157920... * 10^77 | 2^256 | number of values storable with 256 bits |
| | 10^80 | | approx. number of atoms in observable universe |
| [googol](googol.md) | 10^100 | | often used big number |
| Shannon number | 10^120 | | estimated number of possible games in [chess](chess.md) |
| [asankhyeya](asankhyeya.md) | 10^140 | | religious number, often used in [Buddhism](buddhism.md) |
| | 1.340780... * 10^154 | 2^512 | number of values storable with 512 bits |
| | 9.332621... * 10^157 | 100! | possible ways to order 100 objects |
| | 4.65... * 10^185 | | approx. number of Planck volumes in observable universe |
| | 1.797693... * 10^308 | | largest number storable in IEEE-754 64 bit float |
| | 1.797693... * 10^308 | 2^1024 | number of values storable with 1024 bits |
| | 3.231700... * 10^616 | 2^2048 | number of values storable with 2048 bits |
| | 4.023872... * 10^2567| 1000! | possibe ways to order 1000 objects |
| [googolplex](googolplex.md) | 10^(10^100) | 10^googol | another large number, number of genders in 21st century |
| [Graham's number](grahams_number.md)| | g64 | extremely, unimaginably large number, > googolplex |
| TREE(3) | unknown | | yet even larger number, > Graham's number |
| [infinity](infinity.md) | | lim x->0 1/x, 1 + 1 + 1 + ... | not always considered a number, largest possible value |
| [aleph](aleph.md) zero | | beth zero, cardinality(N) | infinite cardinal number, "size" of the set of nat. num.|
| [i](i.md) (imaginary unit) | | j * k | part of complex numbers and quaternions |
| [j](j.md) | | k * i | one of quaternion units |
| [k](k.md) | | i * j | one of quaternion units |
## See Also