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0,1
This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantities and probabilities. Each number is given a name in the short scale, which is used in English-speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language. Smaller than (one googolth) * ''Physics:'' The probability of a human spontaneously teleporting due to quantum effects is approximately 10−4.5×1029. * ''Mathematics – random selections:'' Approximately is a rough first estimate of the probability that a typing "monkey", or an English-illiterate typing robot, when placed in front of a typewriter, will type out William Shakespeare's play ''Hamlet'' as its first set of inputs, on the precondition it typed the needed number of characters. However, demanding correct punctuation, capitalization, and spacing, the probability falls to around 10−360,783. * ''Comput ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinite Monkey Theorem
The infinite monkey theorem states that a monkey hitting keys independently and at randomness, random on a typewriter keyboard for an infinity, infinite amount of time will almost surely type any given text, including the complete works of William Shakespeare. More precisely, under the assumption of independence and randomness of each keystroke, the monkey would almost surely type every possible finite text an infinite number of times. The theorem can be generalized to state that any infinite sequence of independent events whose probabilities are uniformly bounded below by a positive number will almost surely have infinitely many occurrences. In this context, "almost surely" is a mathematical term meaning the event happens with probability 1, and the "monkey" is not an actual monkey, but a metaphor for an Abstract and concrete, abstract device that produces an endless random sequence of letters and symbols. Variants of the theorem include multiple and even infinitely many indepen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithmic Scale
A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences among the magnitudes of the numbers involved. Unlike a linear Scale (measurement), scale where each unit of distance corresponds to the same increment, on a logarithmic scale each unit of length is a multiple of some base value raised to a power, and corresponds to the multiplication of the previous value in the scale by the base value. In common use, logarithmic scales are in base 10 (unless otherwise specified). A logarithmic scale is Nonlinear system, nonlinear, and as such numbers with equal distance between them such as 1, 2, 3, 4, 5 are not equally spaced. Equally spaced values on a logarithmic scale have exponents that increment uniformly. Examples of equally spaced values are 10, 100, 1000, 10000, and 100000 (i.e., 101, 102, 103, 104, 105) and 2, 4, 8, 16, and 32 (i.e., 21, 22, 23, 24, 25). Exponential growt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Precision
Extended precision refers to floating-point number formats that provide greater precision than the basic floating-point formats. Extended-precision formats support a basic format by minimizing roundoff and overflow errors in intermediate values of expressions on the base format. In contrast to ''extended precision'', arbitrary-precision arithmetic refers to implementations of much larger numeric types (with a storage count that usually is not a power of two) using special software (or, rarely, hardware). Extended-precision implementations There is a long history of extended floating-point formats reaching back nearly to the middle of the last century.. Various manufacturers have used different formats for extended precision for different machines. In many cases the format of the extended precision is not quite the same as a scale-up of the ordinary single- and double-precision formats it is meant to extend. In a few cases the implementation was merely a software-based change i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contract Bridge
Contract bridge, or simply bridge, is a trick-taking game, trick-taking card game using a standard 52-card deck. In its basic format, it is played by four players in two Team game, competing partnerships, with partners sitting opposite each other around a table. Millions of people play bridge worldwide in clubs, bridge tournaments, tournaments, online and with friends at home, making it one of the world's most popular card games, particularly among Old Age, seniors. The World Bridge Federation (WBF) is the governing body for international competitive bridge, with numerous other bodies governing it at the regional level. The game consists of a number of , each progressing through four phases. The cards are to the players; then the players ''call'' (or ''bid'') in an seeking to take the , specifying how many tricks the partnership receiving the contract (the declaring side) needs to take to receive points for the deal. During the auction, partners use their bids to exchange infor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quecto-
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The prefix '' kilo'', for example, may be added to ''gram'' to indicate ''multiplication'' by one thousand: one kilogram is equal to one thousand grams. The prefix '' milli'', likewise, may be added to ''metre'' to indicate ''division'' by one thousand; one millimetre is equal to one thousandth of a metre. Decimal multiplicative prefixes have been a feature of all forms of the metric system, with six of these dating back to the system's introduction in the 1790s. Metric prefixes have also been used with some non-metric units. The SI prefixes are metric prefixes that were standardised for use in the International System of Units (SI) by the International Bureau of Weights and Measures (BIPM) in resolutions dating from 1960 to 2022. Since 2009, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single-precision Floating-point Format
Single-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 231 − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 − 2−23) × 2127 ≈ 3.4028235 × 1038. All integers with seven or fewer decimal digits, and any 2''n'' for a whole number −149 ≤ ''n'' ≤ 127, can be converted exactly into an IEEE 754 single-precision floating-point value. In the IEEE 754 standard, the 32-bit base-2 format is officially referred to as binary32; it was called single in IEEE 754-1985. IEEE 754 specifies additional floating-point types, such as 64-bit base-2 ''doubl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial
In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \times (n-3) \times \cdots \times 3 \times 2 \times 1 \\ &= n\times(n-1)!\\ \end For example, 5! = 5\times 4! = 5 \times 4 \times 3 \times 2 \times 1 = 120. The value of 0! is 1, according to the convention for an empty product. Factorials have been discovered in several ancient cultures, notably in Indian mathematics in the canonical works of Jain literature, and by Jewish mystics in the Talmudic book ''Sefer Yetzirah''. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, where its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there In mathematical analysis, factorials are used in power series for the ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard 52-card Deck
The standard 52-card deck of French-suited playing cards is the most common pack of playing cards used today. The main feature of most playing card decks that empower their use in diverse games and other activities is their double-sided design, where one side, usually bearing a colourful or complex pattern, is exactly identical on all playing cards, thus ensuring the anonymity and fungibility of the cards when their value is to be kept secret, and a second side, that, when apparent, is unique to every individual card in a deck, usually bearing a suit as well as an alphanumerical value, which may be used to distinguish the card in game mechanics. In English-speaking countries it is the only traditional pack used for playing cards; in many countries, however, it is used alongside other traditional, often older, standard packs with different suit systems such as those with German-, Italian-, Spanish- or Swiss suits. The most common pattern of French-suited cards worldwide and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shuffling
Shuffling is a technique used to randomize a deck of playing cards, introducing an element of chance into card games. Various shuffling methods exist, each with its own characteristics and potential for manipulation. One of the simplest shuffling techniques is the overhand shuffle, where small packets of cards are transferred from one hand to the other. This method is easy to perform but can be manipulated to control the order of cards. Another common technique is the riffle shuffle, where the deck is split into two halves and interleaved. This method is more complex but minimizes the risk of exposing cards. The Gilbert–Shannon–Reeds model suggests that seven riffle shuffles are sufficient to thoroughly randomize a deck, although some studies indicate that six shuffles may be enough. Other shuffling methods include the Hindu shuffle, commonly used in Asia, and the pile shuffle, where cards are dealt into piles and then stacked. The Mongean shuffle involves a specific seq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal32 Floating-point Format
In computing, decimal32 is a decimal floating-point computer numbering format that occupies 4 bytes (32 bits) in computer memory. Purpose and use Like the binary16 and binary32 formats, decimal32 uses less space than the actually most common format binary64. Range and precision decimal32 supports 'normal' values, which can have 7 digit precision from up to , plus 'subnormal' values with ramp-down relative precision down to (one digit), signed zeros, signed infinities and NaN (Not a Number). The encoding is somewhat complex, see below. The binary format with the same bit-size, binary32, has an approximate range from subnormal-minimum over normal-minimum with full 24-bit precision: to maximum . Encoding of decimal32 values decimal32 values are encoded in a 'not normalized' near to 'scientific format', with combining some bits of the exponent with the leading bits of the significand in a 'combination field'. Besides the special cases infinities and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
