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Number Of Elements
In mathematics, the cardinality of a finite set is the number of its elements, and is therefore a measure of size of the set. Since the discovery by Georg Cantor, in the late 19th century, of different sizes of infinite sets, the term ''cardinality'' was coined for generalizing to infinite sets the concept of the number of elements. More precisely, two sets have the same cardinality if there exists a one-to-one correspondence between them. In the case of finite sets, the common operation of ''counting'' consists of establishing a one-to-one correspondence between a given set and the set of the first natural numbers, for some natural number . In this case, is the cardinality of the set. A set is ''infinite'' if the counting operation never finishes, that is, if its cardinality is not a natural number. The basic example of an infinite set is the set of all natural numbers. The great discovery of Cantor is that infinite sets of apparently different size may have the same cardina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apples And Oranges V2
An apple is a round, edible fruit produced by an apple tree (''Malus'' spp.). Fruit trees of the orchard or domestic apple (''Malus domestica''), the most widely grown in the genus, are cultivated worldwide. The tree originated in Central Asia, where its wild ancestor, ''Malus sieversii'', is still found. Apples have been grown for thousands of years in Eurasia before they were introduced to North America by European colonists. Apples have cultural significance in many mythologies (including Norse and Greek) and religions (such as Christianity in Europe). Apples grown from seeds tend to be very different from those of their parents, and the resultant fruit frequently lacks desired characteristics. For commercial purposes, including botanical evaluation, apple cultivars are propagated by clonal grafting onto rootstocks. Apple trees grown without rootstocks tend to be larger and much slower to fruit after planting. Rootstocks are used to control the speed of growth and the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Post-Classical Latin Language
Late Latin is the scholarly name for the form of Literary Latin of late antiquity.Roberts (1996), p. 537. English dictionary definitions of Late Latin date this period from the 3rd to 6th centuries CE, and continuing into the 7th century in the Iberian Peninsula. This somewhat ambiguously defined version of Latin was used between the eras of Classical Latin and Medieval Latin. Scholars do not agree exactly when Classical Latin should end or Medieval Latin should begin. Being a written language, Late Latin is not the same as Vulgar Latin, or more specifically, the spoken Latin of the post-Imperial period. The latter served as the ancestor of the Romance languages. Although Late Latin reflects an upsurge in the use of Vulgar Latin vocabulary and constructs, it remains largely classical in its overall features, depending on the author who uses it. Some Late Latin writings are more literary and classical, but others are more inclined to the vernacular. As such it is an important ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting (''projective space'') and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "Point at infinity, points at infinity") to Euclidean points, and vice versa. Properties meaningful for projective geometry are respected by this new idea of transformation, which is more radical in its effects than can be expressed by a transformation matrix and translation (geometry), translations (the affine transformations). The first issue for geometers is what kind of geometry is adequate for a novel situation. Unlike in Euclidean geometry, the concept of an angle does not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jakob Steiner
Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry. Life Steiner was born in the village of Utzenstorf, Canton of Bern. At 18, he became a pupil of Heinrich Pestalozzi and afterwards studied at Heidelberg. Then, he went to Berlin, earning a livelihood there, as in Heidelberg, by tutoring. Here he became acquainted with A. L. Crelle, who, encouraged by his ability and by that of Niels Henrik Abel, then also staying at Berlin, founded his famous '' Journal'' (1826). After Steiner's publication (1832) of his ''Systematische Entwickelungen'' he received, through Carl Gustav Jacob Jacobi, who was then professor at Königsberg University, and earned an honorary degree there; and through the influence of Jacobi and of the brothers Alexander and Wilhelm von Humboldt a new chair of geometry was founded for him at Berlin (1834). This he occupied until his death in Bern on 1 April 1863. He was described by Thomas Hirst as follo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serial Numbers
A serial number (SN) is a unique identifier used to ''uniquely'' identify an item, and is usually assigned incrementally or sequentially. Despite being called serial "numbers", they do not need to be strictly numerical and may contain letters and other typographical symbols, or may consist entirely of a character string. Applications of serial numbering Serial numbers identify otherwise identical individual units, thereby serving various practical uses. Serial numbers are a deterrent against theft and counterfeit products, as they can be recorded, and stolen or otherwise irregular goods can be identified. Banknotes and other transferable documents of value bear serial numbers to assist in preventing counterfeiting and tracing stolen ones. They are valuable in quality control, as once a defect is found in the production of a particular batch of product, the serial number will identify which units are affected. Some items with serial numbers are automobiles, firearms, elec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jersey Numbers
In team sports, the number, often referred to as the uniform number, squad number, jersey number, shirt number, sweater number, or similar (with such naming differences varying by sport and region) is the number worn on a player's uniform, to identify and distinguish each player (and sometimes others, such as coaches and officials) from others wearing the same or similar uniforms. The number is typically displayed on the rear of the jersey, often accompanied by the surname. Sometimes it is also displayed on the front and/or sleeves, or on the player's shorts or headgear. It is used to identify the player to officials, other players, official scorers, and spectators; in some sports, it is also indicative of the player's position. The first use of jersey numbers is credited to a football team from New Zealand called the Nelson Football Club, who began wearing numbered jerseys in 1911. The numbers were used to help the spectators identify the players on the field, as well as to hel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nominal Number
Nominal numbers are numerals used as labels to Unique identifier, identify items uniquely. Importantly, the actual values of the numbers which these numerals represent are less relevant, as they do not indicate quantity, rank, or any other measurement. Labelling referees Smith and Kumar as referees "1" and "2" is a use of nominal numbers. Any set of numbers (a subset of the natural numbers) will be consistent labels as long as a ''distinct'' number is uniquely used for each distinct term which needs to be labelled. Nonetheless, sequences of integers may naturally be used as the simplest way to begin labelling; for example, 1, 2, 3, and so on. Definition The term "nominal number" may be quite recent and of limited use. It appears to have originated in school textbooks derived from the statistical term "nominal data", defined as data indicating "...merely statements of qualitative category of membership." This usage comes from the sense of wikt:nominal, nominal as "name". Mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinal Numbers (linguistics)
In linguistics, ordinal numerals or ordinal number words are words representing position or rank in a sequential order; the order may be of size, importance, chronology, and so on (e.g., "third", "tertiary"). They differ from cardinal numerals, which represent quantity (e.g., "three") and other types of numerals. In traditional grammar, all Numeral (linguistics), numerals, including ordinal numerals, are grouped into a separate part of speech (, hence, "noun numeral" in older English grammar books). However, in modern interpretations of English grammar, ordinal numerals are usually conflated with adjectives. Ordinal numbers may be written in English with numerals and letter suffixes: 1st, 2nd or 2d, 3rd or 3d, 4th, 11th, 21st, 101st, 477th, etc., with the suffix acting as an ordinal indicator. Written dates often omit the suffix, although it is nevertheless pronounced. For example: 5 November 1605 (pronounced "the fifth of November ... "); November 5, 1605, ("November (the) F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Etymonline
Etymonline, or ''Online Etymology Dictionary'', sometimes abbreviated as OED (not to be confused with the ''Oxford English Dictionary'', which the site often cites), is a free online dictionary that describes the etymology, origins of English language, English words, written and compiled by Douglas R. Harper. Description Douglas R. Harper is an American Civil War historian and copy editor for LNP Media Group. He compiled the etymology dictionary to record the history and evolution of more than 50,000 words, including slang and technical terms. The core of its etymology information stems from ''The Barnhart Dictionary of Etymology'' by Robert Barnhart, Ernest Klein's ''Comprehensive Etymology Dictionary of the English Language'', ''The Middle English Compendium'', ''The Oxford English Dictionary'', and the 1889–1902 ''Century Dictionary''. Harper also researches on digital archives. On the ''Etymonline'' homepage, Harper says that he considers himself "essentially and for the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford English Dictionary
The ''Oxford English Dictionary'' (''OED'') is the principal historical dictionary of the English language, published by Oxford University Press (OUP), a University of Oxford publishing house. The dictionary, which published its first edition in 1884, traces the historical development of the English language, providing a comprehensive resource to scholars and academic researchers, and provides ongoing descriptions of English language usage in its variations around the world. In 1857, work first began on the dictionary, though the first edition was not published until 1884. It began to be published in unbound Serial (literature), fascicles as work continued on the project, under the name of ''A New English Dictionary on Historical Principles; Founded Mainly on the Materials Collected by The Philological Society''. In 1895, the title ''The Oxford English Dictionary'' was first used unofficially on the covers of the series, and in 1928 the full dictionary was republished in 10 b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinal Numbers (linguistics)
In linguistics, and more precisely in traditional grammar, a cardinal numeral (or cardinal number word) is a part of speech used to count. Examples in English are the words ''one'', ''two'', ''three'', and the compounds ''three hundred ndforty-two'' and ''nine hundred ndsixty''. Cardinal numerals are classified as definite, and are related to ordinal numbers, such as the English ''first'', ''second'', ''third'', etc. See also * Arity * Cardinal number for the related usage in mathematics * English numerals (in particular the ''Cardinal numbers'' section) * Distributive number * Multiplier * Nominal numeral * Numeral for examples of number systems * Ordinal number * Valency * Roman numerals * Latin numerals * Greek numerals Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, is a numeral system, system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal number (linguistics), or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinal Directions
The four cardinal directions or cardinal points are the four main compass directions: north (N), south (S), east (E), and west (W). The corresponding azimuths ( clockwise horizontal angle from north) are 0°, 90°, 180°, and 270°. The four ordinal directions or intercardinal directions are northeast (NE), southeast (SE), southwest (SW), and northwest (NW). The corresponding azimuths are 45°, 135°, 225°, and 315°. The intermediate direction of every pair of neighboring cardinal and intercardinal directions is called a secondary intercardinal direction. These eight shortest points in the compass rose shown to the right are: # West-northwest (WNW) # North-northwest (NNW) # North-northeast (NNE) # East-northeast (ENE) # East-southeast (ESE) # South-southeast (SSE) # South-southwest (SSW) # West-southwest (WSW) Points between the cardinal directions form the points of the compass. Arbitrary horizontal directions may be indicated by their azimuth angle value. Determinatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
