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An arrow is a graphical symbol, such as ←, ↑ or →, or a pictogram, used to point or indicate direction. In its simplest form, an arrow is a triangle, chevron, or concave kite, usually affixed to a line segment or rectangle, and in more complex forms a representation of an actual arrow (e.g. ➵ U+27B5). The direction indicated by an arrow is the one along the length of the line or rectangle toward the single pointed end. History An older (medieval) convention is the manicule (pointing hand, ☚). Pedro Reinel in c. 1505 first used the fleur-de-lis as indicating north in a compass rose; the convention of marking the eastern direction with a cross is older (medieval). Use of the arrow symbol does not appear to pre-date the 18th century. An early arrow symbol is found in an illustration of Bernard Forest de Bélidor's treatise ''L'architecture hydraulique'', printed in France in 1737. The arrow is here used to illustrate the direction of the flow of water and of the wate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manicule
The manicule, , is a typography, typographic mark with the appearance of a hand with its index finger extending in a pointing gesture. Originally used for handwritten marginal notes, it later came to be used in printed works to draw the reader's attention to important text. Though once widespread, it is rarely used today, except as an occasional archaic novelty or on informal directional signs. Terminology For most of its history, the mark has been inconsistently referred to by a variety of names. William H. Sherman, in the first dedicated study of the mark, uses the term ''manicule'' (from the Latin root ''manicula'', meaning "little hand"), but also identifies 14 further names which he records as having been used: * hand * pointing hand * hand director * pointer * digit * fist * mutton fist * bishop's fist * index * * indicator * * maniple (vestment), maniple * pilcrow History Handwritten manicules The symbol originates in scribal tradition of the medieval and Renaissa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A Short History Of The English People
''A Short History of the English People'' is a book written by English historian John Richard Green. Published in 1874, "it is a history, not of English Kings or English Conquests, but of the English People." Background and reception Green began work on the book in 1869, having been given only six months to live after being hit hard by disease that had plagued him throughout his life. Only having around 800 pages to write on, he had to leave out much of what he wanted to include. Green intentionally left out the battles of England feeling they did not play a big role in the formation of the nation, saying that historians "too often turned history into a mere record of the butchery of men by their fellow men." His new ideas, and omission of information that others felt important, meant Green was criticized by other historians as well as the people close to him. Others thought highly of the book, including Francis Adams, who used quotations from the book in his poem ''The Peasant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Equivalence
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending on the notation being used. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related. Logical equivalences In logic, many common logical equivalences exist and are often listed as laws or properties. The following tables illustrate some of these. General logical equivalences Logical equivalences involving conditional statements :#p \rightarrow q \equiv \neg p \vee q :#p \rightarrow q \equiv \neg q \rightarrow \neg p :#p \vee q \equiv \neg p \rightarrow q :#p \wedge q \equiv \neg (p \rightarrow \neg q) :#\neg (p \rightarrow q) \equiv p \wedge \neg q :#(p \righta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). He adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set a course for mathematical research of the 20th century. Hilbert and his students contributed to establishing rigor and developed important tools used in modern mathematical physics. He was a cofounder of proof theory and mathematical logic. Life Early life and education Hilbert, the first of two children and only son of O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Notation
Mathematical notation consists of using glossary of mathematical symbols, symbols for representing operation (mathematics), operations, unspecified numbers, relation (mathematics), relations, and any other mathematical objects and assembling them into expression (mathematics), expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and property (philosophy), properties in a concise, unambiguous, and accurate way. For example, the physicist Albert Einstein's formula E=mc^2 is the quantitative representation in mathematical notation of 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 centuries by René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and overall Leonhard Euler. Symbols and typeface The use of many symbols is the basis of mathematical notation. They play a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical NOR
In Boolean logic, logical NOR, non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form (''p'' NOR ''q'') is true precisely when neither ''p'' nor ''q'' is true—i.e. when both ''p'' and ''q'' are ''false''. It is logically equivalent to \neg(p \lor q) and \neg p \land \neg q, where the symbol \neg signifies logical negation, \lor signifies OR, and \land signifies AND. Non-disjunction is usually denoted as \downarrow or \overline or X (prefix) or \operatorname. As with its dual, the NAND operator (also known as the Sheffer stroke—symbolized as either \uparrow, \mid or /), NOR can be used by itself, without any other logical operator, to constitute a logical formal system (making NOR functionally complete). The computer used in the spacecraft that first carried humans to the moon, the Apollo Guidance Computer, was constructed entirely using NOR gates with three inputs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NAND Operator
In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called non-conjunction, alternative denial (since it says in effect that at least one of its operands is false), or NAND ("not and"). In digital electronics, it corresponds to the NAND gate. It is named after Henry Maurice Sheffer and written as \mid or as \uparrow or as \overline or as Dpq in Polish notation by Łukasiewicz (but not as , , , often used to represent disjunction). Its dual is the NOR operator (also known as the Peirce arrow, Quine dagger or Webb operator). Like its dual, NAND can be used by itself, without any other logical operator, to constitute a logical formal system (making NAND functionally complete). This property makes the NAND gate crucial to modern digital electronics, including its use in computer processor design. Definition Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
If And Only If
In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, ''P if and only if Q'' means that ''P'' is true whenever ''Q'' is true, and the only case in which ''P'' is true is if ''Q'' is also true, whereas in the case of ''P if Q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Material Conditional
The material conditional (also known as material implication) is a binary operation commonly used in logic. When the conditional symbol \to is interpreted as material implication, a formula P \to Q is true unless P is true and Q is false. Material implication is used in all the basic systems of classical logic as well as some nonclassical logics. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many programming languages. However, many logics replace material implication with other operators such as the strict conditional and the variably strict conditional. Due to the paradoxes of material implication and related problems, material implication is not generally considered a viable analysis of conditional sentences in natural language. Notation In logic and related fields, the material conditional is customarily notated with an infix operator \to. The material conditional is also notated using the i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-way Road
A two-way street is a street that allows vehicles to travel in both directions. On most two-way streets, especially main streets, a line is painted down the middle of the road to remind drivers to stay on their side of the road. Sometimes one portion of a street is two-way and the other portion is one-way. If there is no line, a car must stay on the appropriate side and watch for cars coming in the opposite direction and prepare to pull over to let them pass. See also * Dual carriageway * One-way traffic One-way traffic (or uni-directional traffic) is traffic that moves in a single direction. A one-way street is a street either facilitating only one-way traffic, or designed to direct vehicles to move in one direction. One-way streets typicall ... References * {{road-stub Types of roads ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Road Surface Marking
Road surface marking is any kind of device or material that is used on a road surface in order to convey official information; they are commonly placed with road marking machines (also referred to as road marking equipment or pavement marking equipment). They can also be applied in other facilities used by vehicles to mark parking spaces or designate areas for other uses. In some countries and areas (France, Italy, Czech Republic, Slovakia etc.), road markings are conceived as horizontal traffic signs, as opposed to vertical traffic signs placed on posts. Road surface markings are used on paved roadways to provide guidance and information to drivers and pedestrians. Uniformity of the markings is an important factor in minimising confusion and uncertainty about their meaning, and efforts exist to standardise such markings across borders. However, countries and areas categorise and specify road surface markings in different ways—white lines are called white lines mechanical, non ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
