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@ -181,15 +181,15 @@ TODO: what is the best number? maybe top 10? would 10 be in top 10? what's the f
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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:
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- **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.
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- **[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.
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- **[signed](signed.md)**: Allow also negative values which brings up the issue of what representation to use -- nowadays the most common is [two's complement](twos_complement.md).
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- **fixed size**: Most common, each number takes some fixed size in memory, expressed in [bits](bit.md) or [bytes](byte.md) -- this of course determines the maximum number of values and so for example the minimum and maximum storable number.
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- **numeric**: Anything considered a number. In very high level languages there may be just one generic "number" type capable of storing any kind of number, automatically choosing the best representation behind the scenes, dynamically allocating memory as it changes size etc.
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- **[unsigned](unsigned.md)**: Don't allow negative values -- this is sufficient in many situations, more straightforward to implement and can reach higher values in the positive direction.
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- **[signed](signed.md)**: Permit both positive and negative values which brings up the question of what representation to choose -- for integers the most common one nowadays is [two's complement](twos_complement.md).
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- **fixed size**: Most common, each number takes some fixed size in memory, expressed in [bits](bit.md) or [bytes](byte.md) -- this naturally determines the maximum number of possible values and thus also the minimum and maximum representable number. Going beyond or below the range typically results in an [overflow](overflow.md).
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- **8bit**: Can store 256 value (e.g. integers from 0 to 255 or -128 to 127).
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- **16bit**: Can store 65536 values.
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- **32bit**: Can store 4294967296 values.
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- ...
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- **[arbitrary size](arbitrary_size_int.md)**: Can store arbitrarily high/low and/or precise value, take variable amount of memory depending on how much is needed, used only in very specialized cases, may be considerably slower.
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- **[arbitrary size](arbitrary_size_int.md)**: Can store arbitrarily high/low and/or precise value, take variable amount of memory depending on how much is needed, used only in very specialized cases when absurdly high numbers may appear, may be considerably slower due to the overhead and lack of direct hardware support for extremely large numbers.
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- **[integer](int.md)**: Integer values, most common, usually using direct or [two's complement](twos_complement.md) representation.
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- **fractional**: Have higher precision than integers, allow storing fractions, are often used to [approximate](approximation.md) real numbers.
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- **[fixed point](fixed_point.md)**: Are represented by a number with radix point in fixed place, have uniform precision.
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@ -203,91 +203,109 @@ However some programming languages, such as [Lisp](lisp.md), sometimes treat num
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## Notable Numbers
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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).
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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; notes: *&* means base 8, *b3* means base 3).
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| number | value | equal to, AKA | notes |
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| ----------------------------------- | -------------------- | ---------------------------------------- | ------------------------------------------------------- |
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| not a number (NaN, undefined, ...) | none | 1/0, 0^0, tan(pi/2) | error value |
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| minus [infinity](infinity.md) | | | not always considered a number, smallest possible value |
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| |-1.797693... * 10^308 | | smallest number storable in IEEE-754 64 bit float |
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| | -1.797693... * 10^308| | smallest number storable in IEEE-754 64 bit float |
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| | -3.402823... * 10^38 | | smallest number storable in IEEE-754 32 bit float |
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| | -9223372036854776000 | -1 * 2^64 / 2 | minimum two's complement signed 64 bit number |
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| | -2147483648 | -1 * 2^32 / 2 | minimum two's complement signed 32 bit number |
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| minus thirty two thousand seven ... | -32768 | -1 * 2^16 / 2 | minimum two's complement signed 16 bit number |
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| minus one hundred twenty eight | -128 | -1 * 2^7 | minimum value of signed byte (two's complement) |
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| minus/negative one | -1 | i^2, j^2, k^2 | |
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| minus one twelfth | -0.08333... | -1/12 | by some methods the result of 1 + 2 + 3 + ... |
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| "[negative zero](negative_zero.md)" | "-0" | 0 | non-mathematical, sometimes used in programming |
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| [zero](zero.md) | 0 | "-0", e^(i * pi) + 1, lim x->inf 1/x | "nothing", additive identity |
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| [zero](zero.md) (none, nil) | 0 | "-0", e^(i * pi) + 1, lim x->inf 1/x | "nothing", additive identity |
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| epsilon | | 1 / omega | infinitesimal, "infinitely small" non-zero |
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| |4.940656... * 10^-324 | | smallest pos. number storable in IEEE-754 64 bit float |
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| | 4.940656... * 10^-324| | smallest pos. number storable in IEEE-754 64 bit float |
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| | 1.401298... * 10^-45 | | smallest pos. number storable in IEEE-754 32 bit float |
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| | 1.616255... * 10^-35 | | Planck length in meters, smallest "length" in Universe |
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| one eight | 0.125 | 2^-3 | |
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| one fourth | 0.25 | 2^-2 | |
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| one third | 0.333333... | ...1313132 (5-adic) | |
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| one half | 0.5 | 2^-1 | |
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| one eight | 0.125 | 2^-3, 0b0.001, 0x0.2 | |
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| one fourth | 0.25 | 2^-2, 0b0.01, 0x0.4 | |
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| one third | 0.333333... | 3^-1, 0b0.0101010..., ...1313132 (5-adic)| |
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| one half | 0.5 | 2^-1, 0b0.1, 0x0.8 | |
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| one over square root of two | 0.707106... | 1/sqrt(2), sin(pi/4), cos(pi/4), 2^(-1/2)| |
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| [one](one.md) | 1 |2^0, 0!, 0.999..., sqrt(1), I, 0b1, cos(0)| NOT a prime, unit, multiplicative identity |
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| [square root](sqrt.md) of two | 1.414213... | sqrt(2), 2^(1/2), 0b1.0110101 | irrational, diagonal of unit square, important in geom. |
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| supergolden ratio | 1.465571... | solve(x^3 - x^2 - 1 = 0) | similar to golden ratio, bit more difficult to compute |
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|phi ([golden ratio](golden_ratio.md))| 1.618033... | (1 + sqrt(5)) / 2, solve(x^2 - x - 1 = 0)| irrational, visually pleasant ratio, divine proportion |
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| square root of three | 1.732050... | sqrt(3), 3^(1/2), 0b1.1011101 | irrational |
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| [two](two.md) | 2 | 2^1, 2!, 2!!, 0b000010, II, 0b10 | (only even) prime, base of [binary](binary.md) system |
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| square root of pi | 1.772453... | sqrt(pi) | |
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| [two](two.md) (couple, pair) | 2 | 2^1, 2!, 2!!, 0b000010, II, 0b10 | (only even) prime, base of [binary](binary.md) system |
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| [silver ratio](silver_ratio.md) | 2.414213... | 1 + sqrt(2), solve(x^2 - 2 * x - 1 = 0) | similar to golden ratio |
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| [e](e.md) (Euler's number) | 2.718281... | 0b10.1011011 | base of natural [logarithm](log.md) |
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| [three](three.md) | 3 | 2^2 - 1, III, Ob11, 2^1.584... | prime, max. number on 2 bits, regular plane tilings |
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| [pi](pi.md) | 3.141592... | 2 * asin(1), 0b11.0010010 | circle circumference to its diameter, irrational |
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| [four](four.md) | 4 | 2^2, 0b000100, IV, 0b100 |first composite number, min. needed to color planar graph|
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| [five](five.md) | 5 | 3^2 - 2^2, V, 0b101, fib(5) | (twin, triplet) prime, number of platonic solids, Fib. |
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| [six](six.md) | 6 | 3!, 1 * 2 * 3, 1 + 2 + 3, VI, 0b110 | highly composite number, perfect number |
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| [six](six.md) (half dozen) | 6 | 3!, 1 * 2 * 3, 1 + 2 + 3, VI, 0b110 | highly composite number, perfect number |
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| [tau](tau.md) | 6.283185... | 2 * pi, 360 degrees | radians in full circle, defined mostly for convenience |
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| [thrembo](thrembo.md) | ??? | | the hidden number |
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| [seven](seven.md) | 7 | 2^3 - 1, VII, 0b111 |(twin) prime, days in week, max. unsigned n. with 3 bits |
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| [eight](eight.md) | 8 | 2^3, 0b001000, VIII, 0b1000, fib(6) | base of [octal](oct.md) system, 7th Fibonacci number |
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| [seven](seven.md) | 7 | 2^3 - 1, VII, &7, 0b111 |(twin) prime, days in week, max. unsigned n. with 3 bits |
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| [eight](eight.md) | 8 | 2^3, 0b001000, VIII, &10, 0b1000, fib(6) | base of [octal](oct.md) system, 7th Fibonacci number |
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| [nine](nine.md) | 9 | 3^3, 1^3 + 2^3, sqrt(81), IX, 0b1001 | |
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| pi squared | 9.869604... | pi^2 | |
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| [ten](ten.md) | 10 |10^1, 1 + 2 + 3 + 4, X, 0b1010, 2^3.321...| your IQ? :D base of our decimal system |
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| eleven | 11 | XI, 0b1011 | palindromic twin prime |
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| twelve, dozen | 12 | 2 * 2 * 3, XII, 0b1100 | highly composite number |
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| thirteen | 13 | fib(7), XIII, 0b1101 | prime considered unlucky (in west and China), Fib. num. |
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| fourteen | 14 | XIV, 0b1110 | |
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| fifteen | 15 | 2^4 - 1, 0b1111, 0x0f, 1 + 2 + 3 + 4 + 5 | maximum unsigned number storable with 4 bits |
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| [sixteen](sixteen.md) | 16 | 2^4, 4^2, 2^2^2, 0b010000, 0x10, XVI | base of [hexadecimal](hex.md) system |
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| seventeen | 17 | 0b10001, 0x11, XVII | twin&sexy prime, binary palindrome |
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| eighteen | 18 | 0b10010, 0x12, XVIII | |
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| nineteen | 19 | 0b10011, 0x13, XIX | twin&sexy prime |
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| twenty | 20 | 0b10100, 0x14, XX | |
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| eleven | 11 | 0xb, b3(102), &13, 0b1011, XI | palindromic twin prime |
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| twelve (dozen) | 12 | 2 * 2 * 3, 0xc, 0b1100, XII | highly composite number |
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| thirteen (long or devil's dozen) | 13 | fib(7), 0xd, 0b1101, XIII | prime considered unlucky (in west and China), Fib. num. |
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| fourteen | 14 | &112, 0b1110, 0xe, XIV | |
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| fifteen | 15 | 2^4 - 1, 0b1111, 0xf, 1 + 2 + 3 + 4 + 5 | maximum unsigned number storable with 4 bits |
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| [sixteen](sixteen.md) | 16 | 2^4, 4^2, 2^2^2, 0b010000, &20, 0x10, XVI| base of [hexadecimal](hex.md) system |
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| seventeen | 17 | 0b10001, &21, 0x11, XVII | twin&sexy prime, binary palindrome |
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| eighteen | 18 | 0b10010, &22, 0x12, XVIII | |
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| nineteen | 19 | 0b10011, &23, 0x13, XIX | twin&sexy prime |
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| twenty | 20 | 0b10100, &24, 0x14, XX | |
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| twenty one | 21 | 0b10101, 0x15, BB(3), fib(8), 0x15, XXI | maximum number of 1s produced by 3 state Turing Machine |
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| twenty four | 24 | 2 * 2 * 2 * 3, 4!, XXIV |highly composite number, possible ways to order 4 objects|
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| twenty five | 25 | 5^2, sqrt(625), XXV | |
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| thirty one | 31 | 2^5 - 1, 0b11111, 0x1f, XXXI |max. unsigned number storable with 5 bits, Mersenne prime|
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| [thirty two](thirty_two.md) | 32 | 2^5, 0b100000, 0x20, XXXII | number of possible values storable with 5 bits |
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| twenty three | 23 | 0b10111, &27, 0x17, | sexy prime |
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| twenty four | 24 | 2 * 2 * 2 * 3, 4!, 0x18, XXIV |highly composite number, possible ways to order 4 objects|
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| twenty five | 25 | 5^2, sqrt(625), 0x19, XXV | |
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| twenty seven | 27 | 3^3, 0b11011, 0x1b, &33, 0x1b, XXVII | palindrome in base 2 and 8 |
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| twenty nine | 29 | 0b11101, &1002, 0x1d, XXIX | twin&sexy prime |
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| thirty one | 31 | 2^5 - 1, 0b11111, &37, 0x1f, XXXI |max. unsigned number storable with 5 bits, Mersenne prime|
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| [thirty two](thirty_two.md) | 32 | 2^5, 0b100000, &40, 0x20, XXXII | number of possible values storable with 5 bits |
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| thirty three | 33 | 1! + 2! + 3! + 4!, XXXIII | |
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| thirty four | 34 | fib(9), 0x22, XXXIV | Fibonacci number |
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| thirty six | 36 | 2 * 2 * 3 * 3, XXXVI | highly composite number |
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| thirty seven | 37 | 0b100101, 0x25, XXXVII | most commonly picked 1 to 100 "random", permutable prime|
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| forty one | 41 | 0b101001, 0x29, XLI | twin&sexy prime |
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| [forty two](42.md) | 42 | XLII | cringe number, answer to some stuff, unlucky in Japan |
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| forty three | 43 | 0b101011, 0x2b, XLIII | twin&sexy prime |
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| forty seven | 47 | 0b101111, 0x2f, XLVII | sexy prime |
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| forty eight | 48 |2^5 + 2^4, 2 * 2 * 2 * 2 * 3, XLVIII, 0x30| highly composite number |
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| forty nine | 49 | 7^2 | |
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| fifty | 50 | L | |
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| fifty three | 53 | 0b110101, 0x35, LIII | sexy prime |
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| fifty five | 55 | fib(10), 1 + 2 + ... + 10, LV | sum of numbers up to 10, 11th Fibonacci number |
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| fifty nine | 59 | 0b111011, 0x3b, LIX | twin&sexy prime |
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| sixty | 60 | 0x3c, LX | highly composite number, used in time measuring |
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| sixty three | 63 | 2^6 - 1, LXIII | maximum unsigned number storable with 6 bits |
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| [sixty four](sixty_four.md) | 64 | 2^6, LXIV, 0x40 | number of squares on a chess board |
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| [sixty nine](69.md) | 69 | LXIX | sexual position |
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| sixty one | 61 | 0x3d, LXI | twin&sexy prime |
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| sixty three | 63 | 2^6 - 1, 0b111111, &77, 0x3f, LXIII | maximum unsigned number storable with 6 bits |
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| [sixty four](sixty_four.md) | 64 | 2^6, 0b1000000, &100, 0x40, LXIV | number of squares on a chess board |
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| sixty seven | 67 | 0x43, LXVII | sexy prime |
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| [sixty nine](69.md) | 69 | 0x45, LXIX | sexual position |
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| seventy one | 71 | 0x47, LXXI | twin prime |
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| seventy three | 73 | 0b1001001, 0x49, LXXIII | twin&sexy prime, binary palindrome |
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| seventy nine | 79 | 0x4f, LXXIX | sexy prime |
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| eighty one | 81 | 3^4, 9*9, XXCI | |
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| eighty nine | 89 | fib(11), 0x59, LXXXIX | Fibonacci number |
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| eighty three | 83 | LXXXIII | sexy prime |
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| eighty nine | 89 | fib(11), 0x59, LXXXIX | Fibonacci number, sexy prime |
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| ninety six | 96 | 2^5 + 2^6, 5! - 4!, 0x60 | alternative sexual position |
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| ninety seven | 97 | XCVII | sexy prime |
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| one hundred | 100 | 10^2, 0x64, C, 2^6.643... | |
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| one hundred seven | 107 | BB(4), CVII | maximum number of 1s produced by 4 state Turing machine |
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| one hundred twenty | 120 | 5!, C(10,3), CXX | possible ways to order 5 objects, highly composite |
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| one hundred twenty one | 121 | 11^2, CXXI | [palindromic](palindrome.md) |
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| one hundred twenty five | 125 | 5^3, CXXV | |
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| one hundred twenty seven | 127 | 2^7 - 1, 0x7f, 0b01111111, CXXVII | maximum value of signed byte, Mersenne prime |
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| one hundred twenty eight | 128 | 2^7, 0x80, CXXVIII, 10^2.107... | |
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| one hundred forty four | 144 | 12^2, fib(12), CXLIV | 13th Fibonacci number |
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| one hundred twenty seven | 127 | 2^7 - 1, 0b01111111, &177, 0x7f, CXXVII | maximum value of signed byte, Mersenne prime |
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| one hundred twenty eight | 128 | 2^7, 0x80, &200, CXXVIII, 10^2.107... | number of values storable with 7 bits |
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| one hundred forty four (gross) | 144 | 12^2, fib(12), CXLIV | 13th Fibonacci number, 12 dozen |
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| one hundred sixty eight | 168 | 24 * 7, CLXVIII | hours in week |
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| two hundred forty three | 243 | 3^5, 0xf3, CCXLIII | |
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| two hundred fifty five | 255 | 2^8 - 1, 0xff, 0b11111111, CCLV |maximum value of unsigned [byte](byte.md), hex palindrome|
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| two hundred fifty five | 255 | 2^8 - 1, 0b11111111, &377, 0xff, CCLV |maximum value of unsigned [byte](byte.md), hex palindrome|
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| two hundred fifty six | 256 | 2^8, 4^4, 16^2, 0x100, ((2^2)^2)^2, CCLVI| number of values that can be stored in one byte |
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| three hundred forty three | 343 | 7^3, CCCXLIII | palindrome |
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| three hundred sixty | 360 | 2 * 2 * 2 * 3 * 3 * 5, CCCLX | highly composite number, degrees in full circle |
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@ -299,21 +317,22 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
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| six hundred and sixty six | 666 | 0x29a, DCLXVI | number of the beast, palindromic |
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| seven hundred twenty | 720 | 6!, 3!!, DCCXX | possible ways to order 6 objects, highly composite |
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| seven hundred twenty nine | 729 | 3^6, (3^2)^3, DCCXXIX | |
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| one thousand | 1000 | 10^3, M, 0x3e8, 2^9.965... | |
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| one thousand twenty three | 1023 | 2^10 - 1, 0x3ff, MXXIII | largest number storable with 10 bits |
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| one thousand twenty four | 1024 | 2^10, 4^5, 0x400, MXXIV, 10^3.010... | number of values storable with 10 bits |
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| one thousand (grand) | 1000 | 10^3, M, 0x3e8, 2^9.965... | |
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| one thousand twenty three | 1023 | 2^10 - 1, &1777, 0x3ff, MXXIII | largest number storable with 10 bits |
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| one thousand twenty four | 1024 |2^10, 4^5, &2000, 0x400, MXXIV, 10^3.01...| number of values storable with 10 bits |
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| one thousand six hundred eighty | 1680 | 0x690, MDCLXXX | highly composite, often used as horizontal resolution |
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| two thousand forty eight | 2048 | 2^11, 0x800, MMXLVIII | number of values storable with 11 bits |
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|two thousand one hundred eighty seven| 2187 | 3^7, 0x88b, MMCLXXXVII | |
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| two thousand four hundred one | 2401 | 7^4, MMCDI | |
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| three thousand one hundred ... | 3125 | 5^5, MMMCXXV | |
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| three thousand nine hundred ... | 3999 | MMMCMXCIX | largest number that can be written with Roman numerals |
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| four thousand ninety six | 4096 | 2^12, 2^(3^4), 0x1000 | number of values storable with 12 bits |
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| four thousand ninety five | 4095 | 2^12 - 1, &7777, 0xfff | maximum unsigned integer storable with 12 bits |
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| four thousand ninety six | 4096 | 2^12, 2^(3^4), &10000, 0x1000 | number of values storable with 12 bits |
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| five thousand forty | 5040 | 7!, 1 * 2 * ... * 7 | possible ways to order 7 objects |
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| five thousand fifty | 5050 | 1 + 2 + ... + 100 | sum of numbers up to 100 |
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| six thousand five hundred sixty one | 6561 | 3^8, 3^(2^3) | |
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|six thousand seven hundred sixty five| 6765 | fib(20), 0x1a6d | Fibonacci number |
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| ten thousand | 10000 | 10^4, 100^2, 2^13.287... | |
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| ten thousand (myriad) | 10000 | 10^4, 100^2, 2^13.287... | |
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| fifteen thousand six hundred ... | 15625 | 5^6, 0x3d09 | |
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| sixteen thousand eight hundred ... | 16807 | 7^5, 0x41a7 | |
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| nineteen thousand six hundred ... | 19683 | 3^9, 3^(3^3), 0x4ce3 | |
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@ -321,8 +340,8 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
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| forty thousand three hundred twenty | 40320 | 8!, 1 * 2 * ... * 8, 0x9d80 | possible ways to order 8 objects |
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| ... (enough lol) | 59049 | 3^10, 0xe6a9 | |
|
||||
| | 65504 | | largest number storable in IEEE-754 16 bit float |
|
||||
| | 65535 | 2^16 - 1, 0xffff | maximum unsigned number storable with 16 bits |
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||||
| | 65536 | 2^16, 256^2, 0x10000, 2^(2^(2^2)) | number of values storable with 16 bits |
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| | 65535 | 2^16 - 1, &177777, 0xffff | maximum unsigned number storable with 16 bits |
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| | 65536 |2^16, 256^2, &200000, 0x10000, 2^(2^(2^2))| number of values storable with 16 bits |
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| | 72078 | | number of possible chess positions after 4 half moves |
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| | 80085 | | looks like BOOBS |
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| | 86400 | 60 * 60 * 24 | seconds in a day |
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@ -332,13 +351,15 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
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|||
| one [million](million.md) | 1000000 | 10^6, 0xf4240, 2^19.931... | |
|
||||
| | 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) |
|
||||
| | 16777216 | 2^24, 16^6, 0xffffff | number of distinct 24 bit values, no. of RGB24 colors |
|
||||
| | 16777217 | 2^24 + 1, 0x1000000 | min. pos. int. unstorable in 32b float (prec. falls < 1)|
|
||||
| | 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, 0x3b9aca00, 2^29.897... | |
|
||||
| | 9876543210 | 0x4cb016ea | all decimal digits from highest to lowest |
|
||||
| | 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 |
|
||||
|
|
@ -354,13 +375,15 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
|
|||
| bazillion | ??? | | used to just express a very large value |
|
||||
| quadrillion | 1000000000000000 | 10^15 | |
|
||||
| | 6402373705728000 | 18! | possible ways to order 18 objects |
|
||||
| | 9007199254740992 | | precision of IEEE double falls below 1 after this num. |
|
||||
| | 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 |
|
||||
| | 18364758544493064000 | 0xfedcba9876543210 | all hexadecimal digits from highest to lowest |
|
||||
| | 18446744073709551615 | 2^64 - 1, 0xffffffffffffffff | maximum unsigned number storable with 64 bits |
|
||||
| | 18446744073709551616 | 2^64 | number of values storable with 64 bits |
|
||||
| | 43252003274489856000 | | number of possible Rubik's cube configurations |
|
||||
| |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 |
|
||||
|
|
@ -389,7 +412,9 @@ Here is a table of some numbers and "number like objects" worthy of mention, mos
|
|||
|
||||
## See Also
|
||||
|
||||
- [real number](real_number.md)
|
||||
- [pseudonumber](pseudonumber.md)
|
||||
- [not a number](nan.md)
|
||||
- [illegal number](illegal_number.md)
|
||||
- [offensive number](offensive_number.md)
|
||||
- [binary numbers](binary.md)
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue