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Reckon
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 c ...
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Roman Calendar
The Roman calendar was the calendar used by the Roman Kingdom and Roman Republic. The term often includes the Julian calendar established by the reforms of the Roman dictator, dictator Julius Caesar and Roman emperor, emperor Augustus in the late 1stcenturyBC and sometimes includes any system dated by inclusive counting towards months' kalends, nones (calendar), nones, and ides (calendar), ides in the Roman manner. The term usually excludes the Alexandrian calendar of Roman Egypt, which continued the unique months of that land's Egyptian calendar, former calendar; the Byzantine calendar of the Byzantine Empire, later Roman Empire, which usually dated the Roman months in the simple count of the ancient Greek calendars; and the Gregorian calendar, which refined the Julian system to bring it into still closer alignment with the tropical year. Roman dates were counted inclusively forward to the next of three principal days: the first of the month (the kalends), a day shortly befor ...
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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, ...
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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 ...
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Accountancy
Accounting, also known as accountancy, is the measurement, processing, and communication of financial and non financial information about economic entities such as businesses and corporations. Accounting, which has been called the "language of business", measures the results of an organization's economic activities and conveys this information to a variety of stakeholders, including investors, creditors, management, and regulators. Practitioners of accounting are known as accountants. The terms "accounting" and "financial reporting" are often used as synonyms. Accounting can be divided into several fields including financial accounting, management accounting, tax accounting and cost accounting. Financial accounting focuses on the reporting of an organization's financial information, including the preparation of financial statements, to the external users of the information, such as investors, regulators and suppliers; and management accounting focuses on the measurement, an ...
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Mathematical Notation
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous and accurate way. For example, Albert Einstein's equation E=mc^2 is the quantitative representation in mathematical notation of the mass–energy equivalence. Mathematical notation was first introduced by François Viète at the end of the 16th century, and largely expanded during the 17th and 18th century by René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and overall Leonhard Euler. Symbols The use of many symbols is the basis of mathematical notation. They play a similar role as words in natural languages. They may play different roles in mathematical notation similarly as verbs, adjective and nouns play different roles in ...
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Fortnight
A fortnight is a unit of time equal to 14 days (two weeks). The word derives from the Old English term , meaning "" (or "fourteen days," since the Anglo-Saxons counted by nights). Astronomy and tides In astronomy, a ''lunar fortnight'' is half a lunar synodic month, which is equivalent to the mean period between a full moon and a new moon (and vice versa). This is equal to 14.77 days. It gives rise to a lunar fortnightly tidal constituent (see: Long-period tides). Analogs in other languages In many languages, there is no single word for a two-week period, and the equivalent terms "two weeks", "14 days", or "15 days" ( counting inclusively) have to be used. * Celtic languages: in Welsh, the term ''pythefnos'', meaning "15 nights", is used. This is in keeping with the Welsh term for a week, which is ''wythnos'' ("eight nights"). In Irish, the term is ''coicís''. * Similarly, in Greek, the term δεκαπενθήμερο (''dekapenthímero''), meaning "15 days", is used. * T ...
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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 ...
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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. ...
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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 ...
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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 for ...
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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 placing ...
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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 freq ...
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