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Iota (letter)
Iota (; uppercase: Ι, lowercase: ι; ) is the ninth letter of the Greek alphabet. It was derived from the Phoenician letter Yodh. Letters that arose from this letter include the Latin I and J, the Cyrillic І (І, і), Yi (Ї, ї), and Je (Ј, ј), and iotated letters (e.g. Yu (Ю, ю)). In the system of Greek numerals, iota has a value of 10. Iota represents the close front unrounded vowel . In early forms of ancient Greek, it occurred in both long and short versions, but this distinction was lost in Koine Greek. Iota participated as the second element in falling diphthongs, with both long and short vowels as the first element. Where the first element was long, the iota was lost in pronunciation at an early date, and was written in polytonic orthography as iota subscript, in other words as a very small ι under the main vowel. Examples include ᾼ ᾳ ῌ ῃ ῼ ῳ. The former diphthongs became digraphs for simple vowels in Koine Greek.see Koine Greek phonology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as well as consonants. In Archaic Greece, Archaic and early Classical Greece, Classical times, the Greek alphabet existed in Archaic Greek alphabets, many local variants, but, by the end of the 4th century BCE, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today. The letter case, uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , /ς, , , , , , . The Greek alphabet is the ancestor of the Latin script, Latin and Cyrillic scripts. Like Latin and Cyrillic, Greek originally had only a single form of each letter; it developed the letter case distinction between uppercase and lowercase in parallel with Latin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yodh
Yodh (also spelled jodh, yod, or jod) is the tenth letter of the Semitic abjads, including Phoenician Yōd /𐤉, Hebrew Yōd , Aramaic Yod , Syriac Yōḏ ܝ, and Arabic . Its sound value is in all languages for which it is used; in many languages, it also serves as a long vowel, representing . The Phoenician letter gave rise to the Greek Iota (Ι), Latin I and J, Cyrillic І, Coptic (Ⲓ) and Gothic eis . The term yod is often used to refer to the speech sound , a palatal approximant, even in discussions of languages not written in Semitic abjads, as in phonological phenomena such as English "yod-dropping". Origins Yod originated from a hieroglyphic “hand”, or *yad. Hebrew Yod Hebrew spelling: colloquial ;The letter appears with or without a hook on different sans-serif fonts, for example: * Arial, DejaVu Sans, Arimo, Open Sans: * Tahoma, Alef, Heebo: Pronunciation In both Biblical and modern Hebrew, Yod represents a palatal approximant (). As a mate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin Iota
Sample "ɩ" from various typefaces. Latin iota (majuscule: , minuscule: ɩ) is a letter of the Latin alphabet, based on the lowercase of the Greek letter iota (ι). It was formerly used in the International Phonetic Alphabet to represent (the vowel in English "bit"). It was replaced by a small capital I (ɪ) in 1989, but it can still be found in use in some later works. Other variations are used for phonetic transcription: ᵼ ι. has been adopted as a letter in the alphabets of some African languages, such as Gurunɛ, Kabiyé or Mossi. Its capital form has a hook to distinguish it from capital I. The accented italic form ''ɩ'' is very often indistinguishable from the italic letter small I ''i'' in serif In typography, a serif () is a small line or stroke regularly attached to the end of a larger stroke in a letter or symbol within a particular font or family of fonts. A typeface or "font family" making use of serifs is called a serif typeface ... fonts. Reference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ypogegrammeni
The iota subscript is a diacritic mark in the Greek alphabet shaped like a small vertical stroke or miniature iota placed below the letter. It can occur with the vowel letters eta , omega , and alpha . It represents the former presence of an offglide after the vowel, forming a so‐called "long diphthong". Such diphthongs (i.e., )—phonologically distinct from the corresponding normal or "short" diphthongs (i.e., )—were a feature of ancient Greek in the pre-classical and classical eras. The offglide was gradually lost in pronunciation, a process that started already during the classical period and continued during the Hellenistic period, with the result that, from approximately the 1st century BC onwards, the former long diphthongs were no longer distinguished in pronunciation from the simple long vowels (long monophthongs) respectively. During the Roman and Byzantine eras, the iota, now mute, was sometimes still written as a normal letter but was often simply left ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Definite Description
In formal semantics and philosophy of language, a definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun. The definite description is ''proper'' if X applies to a unique individual or object. For example: " the first person in space" and " the 42nd President of the United States of America", are proper. The definite descriptions "the person in space" and "the Senator from Ohio" are ''improper'' because the noun phrase X applies to more than one thing, and the definite descriptions "the first man on Mars" and "the Senator from some Country" are ''improper'' because X applies to nothing. Improper descriptions raise some difficult questions about the law of excluded middle, denotation, modality, and mental content. Russell's analysis As France is currently a republic, it has no king. Bertrand Russell pointed out that this raises a puzzle about the truth value of the sentence "The present King of France is bald." The sen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inclusion Map
In mathematics, if A is a subset of B, then the inclusion map (also inclusion function, insertion, or canonical injection) is the function \iota that sends each element x of A to x, treated as an element of B: \iota : A\rightarrow B, \qquad \iota(x)=x. A "hooked arrow" () is sometimes used in place of the function arrow above to denote an inclusion map; thus: \iota: A\hookrightarrow B. (However, some authors use this hooked arrow for any embedding.) This and other analogous injective functions from substructures are sometimes called natural injections. Given any morphism f between objects X and Y, if there is an inclusion map into the domain \iota : A \to X, then one can form the restriction f \, \iota of f. In many instances, one can also construct a canonical inclusion into the codomain R \to Y known as the range of f. Applications of inclusion maps Inclusion maps tend to be homomorphisms of algebraic structures; thus, such inclusion maps are embeddings. More precisel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imaginary Unit
The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of in a complex number is 2+3i. Imaginary numbers are an important mathematical concept; they extend the real number system \mathbb to the complex number system \mathbb, in which at least one root for every nonconstant polynomial exists (see Algebraic closure and Fundamental theorem of algebra). Here, the term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1: and -i, just as there are two complex square roots of every real number other than zero (which has one double square root). In contexts in which use of the letter is ambiguous or problematic, the letter or the Greek \iota is sometimes used instead. For example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Go (programming Language)
Go is a statically typed, compiled programming language designed at Google by Robert Griesemer, Rob Pike, and Ken Thompson. It is syntactically similar to C, but with memory safety, garbage collection, structural typing, and CSP-style concurrency. It is often referred to as Golang because of its former domain name, golang.org, but its proper name is Go. There are two major implementations: * Google's self-hosting "gc" compiler toolchain, targeting multiple operating systems and WebAssembly. * gofrontend, a frontend to other compilers, with the ''libgo'' library. With GCC the combination is gccgo; with LLVM the combination is gollvm. A third-party source-to-source compiler, GopherJS, compiles Go to JavaScript for front-end web development. History Go was designed at Google in 2007 to improve programming productivity in an era of multicore, networked machines and large codebases. The designers wanted to address criticism of other languages in use at Google, but keep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
APL (programming Language)
APL (named after the book ''A Programming Language'') is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the Array data type#Multi-dimensional arrays, multidimensional array. It uses a large range of APL syntax and symbols, special graphic symbols to represent most functions and operators, leading to very concise code. It has been an important influence on the development of concept modeling, spreadsheets, functional programming, and computer math packages. It has also inspired several other programming languages. History Mathematical notation A mathematical notation for manipulating arrays was developed by Kenneth E. Iverson, starting in 1957 at Harvard University. In 1960, he began work for IBM where he developed this notation with Adin Falkoff and published it in his book ''A Programming Language'' in 1962. The preface states its premise: This notation was used inside IBM for short research reports on computer systems, such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A+ (programming Language)
A+ is a high-level, interactive, interpreted array programming language designed for numerically intensive applications, especially those found in financial applications. History In 1985, Arthur Whitney created the A programming language to replace APL. Other developers at Morgan Stanley extended it to A+, adding a graphical user interface and other language features. The graphical user interface A+ was released in 1988. Arthur Whitney went on to create a proprietary array language named K. Like J, K omits the APL character set. It lacks some of the perceived complexities of A+, such as the existence of statements and two different modes of syntax. Features A+ provides an extended set of functions and operators, a graphical user interface with automatic synchronizing of widgets and variables, asynchronous executing of functions associated with variables and events, dynamic loading of user compiled subroutines, and other features. A+ runs on many Unix variants, incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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