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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) * ''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. * ''Computing:'' 2.2 is approximately equal to the smallest positive non-zero value that can be represented by an octuple-precision ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinite Monkey Theorem
The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, such as the complete works of William Shakespeare. In fact, the monkey would almost surely type every possible finite text an infinite number of times. However, the probability that monkeys filling the entire observable universe would type a single complete work, such as Shakespeare's ''Hamlet'', is so tiny that the chance of it occurring during a period of time hundreds of thousands of orders of magnitude longer than the age of the universe is ''extremely'' low (but technically not zero). The theorem can be generalized to state that any sequence of events which has a non-zero probability of happening will almost certainly eventually occur, given enough time. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."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, . The higher the probability of an event, the more likely it is that the event will occur. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithmic Scale
A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a scale is nonlinear: the numbers 10 and 20, and 60 and 70, are not the same distance apart on a log scale. Rather, the numbers 10 and 100, and 60 and 600 are equally spaced. Thus moving a unit of distance along the scale means the number has been ''multiplied'' by 10 (or some other fixed factor). Often exponential growth curves are displayed on a log scale, otherwise they would increase too quickly to fit within a small graph. Another way to think about it is that the ''number of digits'' of the data grows at a constant rate. For example, the numbers 10, 100, 1000, and 10000 are equally spaced on a log scale, because their numbers of digits is going up by 1 each time: 2, 3, 4, and 5 digits. In this way, adding two digits ''multiplies'' the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal64 Floating-point Format
In computing, decimal64 is a decimal floating-point computer numbering format that occupies 8 bytes (64 bits) in computer memory. It is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations. Decimal64 supports 16 decimal digits of significand and an exponent range of −383 to +384, i.e. to . (Equivalently, to .) In contrast, the corresponding binary format, which is the most commonly used type, has an approximate range of to . Because the significand is not normalized, most values with less than 16 significant digits have multiple possible representations; , etc. Zero has 768 possible representations (1536 if both signed zeros are included). Decimal64 floating point is a relatively new decimal floating-point format, formally introduced in the 2008 version of IEEE 754 as well as with ISO/IEC/IEEE 60559:2011. Representation of decimal64 values IEEE 754 allows two alternative representation methods ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Suit (cards)
In playing cards, a suit is one of the categories into which the cards of a deck are divided. Most often, each card bears one of several pips (symbols) showing to which suit it belongs; the suit may alternatively or additionally be indicated by the color printed on the card. The rank for each card is determined by the number of pips on it, except on face cards. Ranking indicates which cards within a suit are better, higher or more valuable than others, whereas there is no order between the suits unless defined in the rules of a specific card game. In a single deck, there is exactly one card of any given rank in any given suit. A deck may include special cards that belong to no suit, often called jokers. History Modern Western playing cards are generally divided into two or three general suit-systems. The older Latin suits are subdivided into the Italian and Spanish suit-systems. The younger Germanic suits are subdivided into the German and Swiss suit-systems. The French suits a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contract Bridge
Contract bridge, or simply bridge, is a trick-taking card game using a standard 52-card deck. In its basic format, it is played by four players in two competing partnerships, with partners sitting opposite each other around a table. Millions of people play bridge worldwide in clubs, tournaments, online and with friends at home, making it one of the world's most popular card games, particularly among 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 dealt to the players; then the players ''call'' (or ''bid'') in an auction 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 also exchange information about their hands, including o ... [...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 7 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 754-2008 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 ''double prec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial
In mathematics, the factorial of a non-negative denoted is the 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 exponential function an ... [...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. In English-speaking countries it is the only traditional pack used for playing cards; in many countries of the world, 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 only one commonly available in Britain and the United States is the English pattern pack. The second most common is the Belgian-Genoese pattern, designed in France, but whose use spread to Spain, Italy, the Ottoman Empire, the Balkans and much of North Africa and the Middle East.''Pattern Sheet 80'' at i-p-c-s.org. Retrieved 23 August 2020. In addition to those, there are other major in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shuffling
Shuffling is a procedure used to randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut, to help ensure that the shuffler has not manipulated the outcome. __TOC__ Techniques Overhand One of the easiest shuffles to accomplish after a little practice is the overhand shuffle. Johan Jonasson wrote, "The overhand shuffle... is the shuffling technique where you gradually transfer the deck from, say, your right hand to your left hand by sliding off small packets from the top of the deck with your thumb." In detail as normally performed, with the pack initially held in the left hand (say), most of the cards are grasped as a group from the bottom of the pack between the thumb and fingers of the right hand and lifted clear of the small group that remains in the left hand. Small packets are then released from the right hand a packet at a time so that they drop on the top of the pack accumulating in the left hand. The process ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Card Shuffle
Shuffling is a procedure used to randomize a deck of playing cards to provide an element of chance in card games. Shuffling is often followed by a cut, to help ensure that the shuffler has not manipulated the outcome. __TOC__ Techniques Overhand One of the easiest shuffles to accomplish after a little practice is the overhand shuffle. Johan Jonasson wrote, "The overhand shuffle... is the shuffling technique where you gradually transfer the deck from, say, your right hand to your left hand by sliding off small packets from the top of the deck with your thumb." In detail as normally performed, with the pack initially held in the left hand (say), most of the cards are grasped as a group from the bottom of the pack between the thumb and fingers of the right hand and lifted clear of the small group that remains in the left hand. Small packets are then released from the right hand a packet at a time so that they drop on the top of the pack accumulating in the left hand. The process ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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