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Counting
Counting is the process of determining the number of elements of a finite set of objects, i.e., determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counter was set to one after the first object, the value after visiting the final object gives the desired number of elements. The related term '' enumeration'' refers to uniquely identifying the elements of a finite (combinatorial) set or infinite set by assigning a number to each element. Counting sometimes involves numbers other than one; for example, when counting money, counting out change, "counting by twos" (2, 4, 6, 8, 10, 12, ...), or "counting by fives" (5, 10, 15, 20, 25, ...). There is archaeological evidence suggesting that humans have been count ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finger Counting
Finger-counting, also known as dactylonomy, is the act of counting using one's fingers. There are multiple different systems used across time and between cultures, though many of these have seen a decline in use because of the spread of Arabic numerals. Finger-counting can serve as a form of manual communication, particularly in marketplace trading – including hand signaling during open outcry in floor trading – and also in games such as morra. Finger-counting is known to go back to ancient Egypt at least, and probably even further back. Georges Ifrah notes that humans learned to count on their hands. Ifrah shows, for example, a picture of Boethius (who lived 480–524 or 525) reckoning on his fingers in . notes that as early as the 3rd millennium BCE, in Egypt's Old Kingdom, in the Pyramid texts' "Spell for obtaining a ferry-boat", the ferryman might object "Did you bring me a man who cannot number his fingers?". This spell was needed to cross a canal of the nether-world ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tally Marks
Tally marks, also called hash marks, are a unary numeral system ( arguably). They are a form of numeral used for counting. They are most useful in counting or tallying ongoing results, such as the score in a game or sport, as no intermediate results need to be erased or discarded. However, because of the length of large numbers, tallies are not commonly used for static text. Notched sticks, known as tally sticks, were also historically used for this purpose. Early history Counting aids other than body parts appear in the Upper Paleolithic. The oldest tally sticks date to between 35,000 and 25,000 years ago, in the form of notched bones found in the context of the European Aurignacian to Gravettian and in Africa's Late Stone Age. The so-called ''Wolf bone'' is a prehistoric artifact discovered in 1937 in Czechoslovakia during excavations at Vestonice, Moravia, led by Karl Absolon. Dated to the Aurignacian, approximately 30,000 years ago, the bone is marked with 55 marks ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abacus
The abacus (''plural'' abaci or abacuses), also called a counting frame, is a calculating tool which has been used since ancient times. It was used in the ancient Near East, Europe, China, and Russia, centuries before the adoption of the Hindu-Arabic numeral system. The exact origin of the abacus has not yet emerged. It consists of rows of movable beads, or similar objects, strung on a wire. They represent digits. One of the two numbers is set up, and the beads are manipulated to perform an operation such as addition, or even a square or cubic root. In their earliest designs, the rows of beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation. Abacuses are still made, often as a bamboo frame with beads sliding on wires. In the ancient world, particularly before the introduction of positional notation, abacuses were a practical calculating tool. The abacus is still used to te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finger Binary
Finger binary is a system for counting and displaying binary numbers on the fingers of either or both hands. Each finger represents one binary digit or bit. This allows counting from zero to 31 using the fingers of one hand, or 1023 using both: that is, up to 25−1 or 210−1 respectively. Using all ten toes as well would theoretically increase this to 1,048,575, but it seems unlikely that many people have the dexterity for this. Modern computers typically store values as some whole number of 8-bit bytes, making the fingers of both hands together equivalent to 1 bytes of storage—in contrast to less than half a byte when using ten fingers to count up to 10.Since computers typically store data in a minimum size of one whole byte, fractions of a byte are used here only for comparison. Mechanics In the binary number system, each numerical digit has two possible states (0 or 1) and each successive digit represents an increasing power of two. Note: What follows is but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brian Butterworth
Brian Lewis Butterworth FBA (born 3 January 1944) is emeritus professor of cognitive neuropsychology in the Institute of Cognitive Neuroscience at University College London, England. His research has ranged from speech errors and pauses, short-term memory deficits, reading and the dyslexias both in alphabetic scripts and Chinese, and mathematics and dyscalculia. He has also pioneered educational neuroscience, notably in the study of learners with special educational needs (''Educational Neuroscience'', 2013). He read psychology and philosophy at Oxford University (1963-1966). He completed an MA on Gödel's theorem at Sussex University (1967-1968) under the direction of Peter Nidditch, and a PhD in psycholinguistics at UCL supervised by Frieda Goldman-Eisler, the first professor of psycholinguistics in the UK. Psycholinguistics His early work, following Goldman-Eisler's pioneering studies, explored the functions of pauses in speech. He confirmed that pauses are required ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Taxation In The United Kingdom
The history of taxation in the United Kingdom includes the history of all collections by governments under law, in money or in kind, including collections by monarchs and lesser feudal lords, levied on persons or property subject to the government, with the primary purpose of raising revenue. Background Prior to the formation of the United Kingdom in 1707, taxation had been levied in the countries that joined to become the UK. For example, in England, King John introduced an export tax on wool in 1203 and King Edward I introduced taxes on wine in 1275. Also in England, a Poor Law tax was established in 1572 to help the deserving poor, and then changed from a local tax to a national tax in 1601. In June 1628, England's Parliament passed the Petition of Right which among other measures, prohibited the use of taxes without its agreement. This prevented the Crown from creating arbitrary taxes and imposing them upon subjects without consultation. One of the key taxes introduced by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sennight
A week is a unit of time equal to seven days. It is the standard time period used for short cycles of days in most parts of the world. The days are often used to indicate common work days and rest days, as well as days of worship. Weeks are often mapped against yearly calendars, but are typically not the basis for them, as weeks are not based on astronomy. The modern seven-day week can be traced back to the Babylonians, who used it within their calendar. Other ancient cultures had different week lengths, including ten in Egypt and an eight-day week for Etruscans. The Etruscan week was adopted by the Ancient Romans, but they later moved to a seven-day week, which had spread across Western Asia and the Eastern Mediterranean. In 321 AD, Emperor Constantine officially decreed a seven-day week in the Roman Empire, including making Sunday a public holiday. This later spread across Europe, then the rest of the world. In English, the names of the days of the week are Monday, Tuesday, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phalanges
The phalanges (singular: ''phalanx'' ) are digital bones in the hands and feet of most vertebrates. In primates, the thumbs and big toes have two phalanges while the other digits have three phalanges. The phalanges are classed as long bones. Structure The phalanges are the bones that make up the fingers of the hand and the toes of the foot. There are 56 phalanges in the human body, with fourteen on each hand and foot. Three phalanges are present on each finger and toe, with the exception of the thumb and large toe, which possess only two. The middle and far phalanges of the fifth toes are often fused together (symphalangism). The phalanges of the hand are commonly known as the finger bones. The phalanges of the foot differ from the hand in that they are often shorter and more compressed, especially in the proximal phalanges, those closest to the torso. A phalanx is named according to whether it is proximal, middle, or distal and its associated finger or toe. The proxim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One-to-one Correspondence
In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. There are no unpaired elements. In mathematical terms, a bijective function is a one-to-one (injective) and onto (surjective) mapping of a set ''X'' to a set ''Y''. The term ''one-to-one correspondence'' must not be confused with ''one-to-one function'' (an injective function; see figures). A bijection from the set ''X'' to the set ''Y'' has an inverse function from ''Y'' to ''X''. If ''X'' and ''Y'' are finite sets, then the existence of a bijection means they have the same number of elements. For infinite sets, the picture is more complicated, leading to the concept of cardinal number—a way to distinguish the various sizes of infinite sets ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subitize
Subitizing is the rapid, accurate, and confident judgments of numbers performed for small numbers of items. The term was coined in 1949 by E. L. Kaufman et al., and is derived from the Latin adjective '' subitus'' (meaning "sudden") and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range. Sets larger than about four items cannot be subitized unless the items appear in a pattern with which the person is familiar (such as the six dots on one face of a die). Large, familiar sets might be counted one-by-one (or the person might calculate the number through a rapid calculation if they can mentally group the elements into a few small sets). A person could also estimate the number of a large set—a skill similar to, but different from, subitizing. The accuracy, speed, and confidence with which observers make judgments of the number of items are critically dependent on the number of ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music," the use of which is "common in most musical systems." The interval between the first and second harmonics of the harmonic series is an octave. In Western music notation, notes separated by an octave (or multiple octaves) have the same name and are of the same pitch class. To emphasize that it is one of the perfect intervals (including unison, perfect fourth, and perfect fifth), the octave is designated P8. Other interval qualities are also possible, though rare. The octave above or below an indicated note is sometimes abbreviated ''8a'' or ''8va'' ( it, all'ottava), ''8va bassa'' ( it, all'ottava bassa, sometimes also ''8vb''), or simply ''8'' for the octave in the direction indicated by pl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interval (music)
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord. In Western music, intervals are most commonly differences between notes of a diatonic scale. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C and D. Intervals can be arbitrarily small, and even imperceptible to the human ear. In physical terms, an interval is the ratio between two sonic f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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