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iota | A Wisdom Archive on iota | | iota A selection of articles related to iota | |
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iota, Iota
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ARTICLES RELATED TO iota | |
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| | |  iota: Encyclopedia II - Permutation - Counting permutationsIn this section only, the traditional definition is used: a permutation is an ordered list without repetitions, perhaps missing some elements. It is easy to count the number of permutations of size r when chosen from a set of size n (with r≤n).
For example, if we have a total of 10 elements, the integers {1, 2, ..., 10}, a permutation of three elements from this set is (5, 3, 4). In this case, n = 10 and r = 3. So how many ways can this completely be done?
We can pretend to sele ...
See also:Permutation, Permutation - Arrangements and substitutions, Permutation - Counting permutations, Permutation - Abstract algebra, Permutation - Notation, Permutation - More details, Permutation - Special permutations, Permutation - Permutations in computing, Permutation - Numbering permutations Read more here: » Permutation: Encyclopedia II - Permutation - Counting permutations |
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| | | | iota: Encyclopedia II - I - History The letter I derived from the Greek iota (Ι, ι). It stood for the vowel /i/, the same as in the Old Italic alphabet. In Latin (as in Modern Greek) /j/ (as English Y in YOKE) was added. In Semitic, /j/ was the usual sound value of Jôd (probably originally a pictogram for an arm with hand), /i/ only in foreign words.
In English, I represents different sounds, among them a diphthong that developed from /i:/ as well as short, open /I/ as in BILL. The dot over the lowercase 'i' is sometimes called a tittle. In the Turkish alphabet, dotted and dotless I are considered separate letters and both have uppercase (I, İ) ...
See also:I, I - History, I - Alternative representations, I - Computing, I - Meanings for I Read more here: » I: Encyclopedia II - I - History |
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| | | | iota: Encyclopedia II - Trinity - Ontology of the Trinity
Trinity - Historical view and usage.
The Trinitarian view has been affirmed as an article of faith by the Nicene (325/381) and Athanasian creeds (circa 500), which attempted to standardize belief in the face of disagreements on the subject. These creeds were formulated and ratified by the Church of the third and fourth centuries in reaction to heterodox theologies, usually involving the nature of the Trinity and/or Christ's position in it. The Nicene-Constantinopolitan Creed (381 version) is still affirmed by Ort ...
See also:Trinity, Trinity - Scripture and tradition, Trinity - Baptism as the beginning lesson, Trinity - Scriptural texts cited as implicit support for the doctrine of the Trinity, Trinity - Ontology of the Trinity, Trinity - Historical view and usage, Trinity - One God, Trinity - God exists in three persons, Trinity - Orthodox Roman Catholic and Protestant distinctions, Trinity - Historical development, Trinity - Dissent from the doctrine, Trinity - Other views of the Trinity, Trinity - Theory of pagan origin and influence, Trinity - Christian life and the Blessed Trinity, Trinity - Similarities in the 16th-century Jewish Kabbalah, Trinity - In popular culture Read more here: » Trinity: Encyclopedia II - Trinity - Ontology of the Trinity |
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| | | | iota: Encyclopedia II - Imaginary unit - i and −i The above equation actually has two distinct solutions which are additive inverses. More precisely, once a solution i of the equation has been fixed, −i (≠ i) is also a solution. Since the equation is the only definition of i, it appears that the definition is ambiguous (more precisely, not well-defined). However, no ambiguity results, as long as we choose a solution and fix it forever as "positive i".
The issue is a subtle one. The most precise explanation is to say that although the comp ...
See also:Imaginary unit, Imaginary unit - Definition, Imaginary unit - i and −i, Imaginary unit - Warning, Imaginary unit - Powers of i, Imaginary unit - i and Euler's formula, Imaginary unit - Alternate notation Read more here: » Imaginary unit: Encyclopedia II - Imaginary unit - i and −i |
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| | | | iota: Encyclopedia II - Iotation - Iotified Cyrillic letters In the Cyrillic alphabet, some letter forms are iotified, that is, formed as a ligature of Early Cyrillic I (І) and a vowel.
In old inscriptions, other iotified letters, even consonants, could be found, but these are not parts of a regular alphabet.
There are more letters which serve the same function, but their glyphs are not made in the same way.
...
See also:Iotation, Iotation - Iotified Cyrillic letters, Iotation - Cyrillic letters for iotated sounds Read more here: » Iotation: Encyclopedia II - Iotation - Iotified Cyrillic letters |
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| | | | iota: Encyclopedia II - Trinity - Ontology of the Trinity
Trinity - Historical view and usage.
The Trinitarian view has been affirmed as an article of faith by the Nicene (325/381) and Athanasian creeds (circa 500), which attempted to standardize belief in the face of disagreements on the subject. These creeds were formulated and ratified by the Church of the third and fourth centuries in reaction to heterodox theologies, usually involving the nature of the Trinity and/or Christ's position in it. The Nicene-Constantinopolitan Creed (381 version) is still affirmed by Ort ...
See also:Trinity, Trinity - Scripture and tradition, Trinity - Baptism as the beginning lesson, Trinity - Key scriptural texts cited by trinitarians, Trinity - Ontology of the Trinity, Trinity - Historical view and usage, Trinity - One God, Trinity - God exists in three persons, Trinity - Orthodox Roman Catholic and Protestant distinctions, Trinity - Historical development, Trinity - Dissent from the doctrine, Trinity - Other views of the Trinity, Trinity - Theory of pagan origin and influence, Trinity - Christian life and the Blessed Trinity, Trinity - Similarities in the 16th-century Jewish Kabbalah, Trinity - In popular culture Read more here: » Trinity: Encyclopedia II - Trinity - Ontology of the Trinity |
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| | | | iota: Encyclopedia II - Trinity - In popular culture In the Valérian comics, the Trinity appeared as a tough, street-hardened police sergeant (Father), a hippie (Son) and a broken jukebox (Holy Spirit).
In the Fritz Lang film Metropolis, the city mayor Joh Fredersen represents the Father and the humble city proletariat as the Holy Spirit. The son of the mayor, Freder Fredersen, represents the Son. The film ends in statement: The intermediator between brain [Father] and ...
See also:Trinity, Trinity - Scripture and tradition, Trinity - Baptism as the beginning lesson, Trinity - Key scriptural texts cited by trinitarians, Trinity - Ontology of the Trinity, Trinity - Historical view and usage, Trinity - One God, Trinity - God exists in three persons, Trinity - Orthodox Roman Catholic and Protestant distinctions, Trinity - Historical development, Trinity - Dissent from the doctrine, Trinity - Other views of the Trinity, Trinity - Theory of pagan origin and influence, Trinity - Christian life and the Blessed Trinity, Trinity - Similarities in the 16th-century Jewish Kabbalah, Trinity - In popular culture Read more here: » Trinity: Encyclopedia II - Trinity - In popular culture |
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| | | | iota: Encyclopedia II - Permutation - Arrangements and substitutions An arrangement is a placement of a set's elements into definite positions (i.e. first, second, etc.), such as {1, 2, 3, 4, 5, 6} arranged as (2, 1, 6, 5, 4, 3). A substitution is a set of replacements of one element for another, but with no elements eliminated in the result; for instance, if you took {1, 2, 3, 4, 5, 6} and substituted 1 with 3, 3 with 4, and 4 with 1, no elements would be eliminated and you'd have one substitution.
Both arrangements and substitutions are commonly called permutations. In mathematics, however, the phras ...
See also:Permutation, Permutation - Arrangements and substitutions, Permutation - Counting permutations, Permutation - Abstract algebra, Permutation - Notation, Permutation - More details, Permutation - Special permutations, Permutation - Permutations in computing, Permutation - Numbering permutations Read more here: » Permutation: Encyclopedia II - Permutation - Arrangements and substitutions |
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| | | | iota: Encyclopedia II - Trinity - In popular culture In the Valérian comics, the Trinity appeared as a tough, street-hardened police sergeant (Father), a hippie (Son) and a broken jukebox (Holy Spirit).
In the Fritz Lang film Metropolis, the city mayor Joh Fredersen represents the Father and the humble city proletariat as the Holy Spirit. The son of the mayor, Freder Fredersen, represents the Son. The film ends in statement: The intermediator between brain [Father] and ...
See also:Trinity, Trinity - Scripture and tradition, Trinity - Baptism as the beginning lesson, Trinity - Scriptural texts cited as implicit support for the doctrine of the Trinity, Trinity - Ontology of the Trinity, Trinity - Historical view and usage, Trinity - One God, Trinity - God exists in three persons, Trinity - Orthodox Roman Catholic and Protestant distinctions, Trinity - Historical development, Trinity - Dissent from the doctrine, Trinity - Other views of the Trinity, Trinity - Theory of pagan origin and influence, Trinity - Christian life and the Blessed Trinity, Trinity - Similarities in the 16th-century Jewish Kabbalah, Trinity - In popular culture Read more here: » Trinity: Encyclopedia II - Trinity - In popular culture |
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| | | | iota: Encyclopedia II - Trinity - Similarities in the 16th-century Jewish Kabbalah In the late Kabbalistic tradition, originating in the city of Safed in the 16th century, an essential part of representations of the Tree of life or Etz Hayim is a set of three vertical lines of light, each line being headed by Sefirot, or degrees of altruistic quality at the top. These three Sefirot form a spiritual or heavenly triangle, which rules the whole earthly part of the Tree of Life. It is obvious that Sefirot of Kether (Crown), Chochmah (Wisdom) and Binah (Understanding), i.e. Ancient One, Father and Mother, or even Chochmah, Bina ...
See also:Trinity, Trinity - Scripture and tradition, Trinity - Baptism as the beginning lesson, Trinity - Scriptural texts cited as implicit support for the doctrine of the Trinity, Trinity - Ontology of the Trinity, Trinity - Historical view and usage, Trinity - One God, Trinity - God exists in three persons, Trinity - Orthodox Roman Catholic and Protestant distinctions, Trinity - Historical development, Trinity - Dissent from the doctrine, Trinity - Other views of the Trinity, Trinity - Theory of pagan origin and influence, Trinity - Christian life and the Blessed Trinity, Trinity - Similarities in the 16th-century Jewish Kabbalah, Trinity - In popular culture Read more here: » Trinity: Encyclopedia II - Trinity - Similarities in the 16th-century Jewish Kabbalah |
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| | | | iota: Encyclopedia II - Permutation - Notation The cycle notation (1 5 2) (3 4) means that 1 is mapped to 5, 5 to 2, 2 to 1, 3 to 4, and 4 to 3. Note that if objects 1,2,3,4,5 are rearranged into the order 2,5,4,3,1, two permutations are involved: (1 5 2) (3 4) mapping the original to the final position of each object, and (1 2 5) (3 4) mapping the old to the new object at any position. The two permutations are each other's inverse.
Notation (1 5 2) implies that 3 and 4 are not changed. For the identity various notations are ...
See also:Permutation, Permutation - Arrangements and substitutions, Permutation - Counting permutations, Permutation - Abstract algebra, Permutation - Notation, Permutation - More details, Permutation - Special permutations, Permutation - Permutations in computing, Permutation - Numbering permutations Read more here: » Permutation: Encyclopedia II - Permutation - Notation |
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| | | | iota: Encyclopedia II - Permutation - More details There are two main notations for such permutations. In relation notation, one can just arrange the "natural" ordering of the elements being permuted on a row, and the new ordering on another row:
This means that in the first position, the second element of the set should be placed, in the second position, the fifth element in the set should be placed, and so on. Alternatively, if we have a finite set of elements (which need not be integers), we can firstly create an association between each element and an integer. ...
See also:Permutation, Permutation - Arrangements and substitutions, Permutation - Counting permutations, Permutation - Abstract algebra, Permutation - Notation, Permutation - More details, Permutation - Special permutations, Permutation - Permutations in computing, Permutation - Numbering permutations Read more here: » Permutation: Encyclopedia II - Permutation - More details |
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| | | | iota: Encyclopedia II - Trinity - Scripture and tradition The word Trinity comes from the Latin noun Trinitas, meaning the state or condition of being three, or a group of three persons or things. The first recorded application of this Latin word to Father, Son and Holy Spirit was by Tertullian in about 200. The Greek term with the same meaning, Τρίας, has given the English word triad. The Sanskrit word, Trimurti, has a similar meaning.
The earliest Christians were noted for their insistence on the oneness of God, in contrast to the polytheism of the p ...
See also:Trinity, Trinity - Scripture and tradition, Trinity - Baptism as the beginning lesson, Trinity - Scriptural texts cited as implicit support for the doctrine of the Trinity, Trinity - Ontology of the Trinity, Trinity - Historical view and usage, Trinity - One God, Trinity - God exists in three persons, Trinity - Orthodox Roman Catholic and Protestant distinctions, Trinity - Historical development, Trinity - Dissent from the doctrine, Trinity - Other views of the Trinity, Trinity - Theory of pagan origin and influence, Trinity - Christian life and the Blessed Trinity, Trinity - Similarities in the 16th-century Jewish Kabbalah, Trinity - In popular culture Read more here: » Trinity: Encyclopedia II - Trinity - Scripture and tradition |
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| | | | iota: Encyclopedia II - Permutation - Permutations in computing Some of the older textbooks do look at permutations as assignments, as mentioned above. In computer science terms, these are assignment operations, with values
1, 2, ..., n
assigned to variables
x1, x2, ..., xn.
Each value should be assigned just once.
The assignment/substitution difference is then illustrative of one way in which functional programming and imperative programming differ — pure functional p ...
See also:Permutation, Permutation - Arrangements and substitutions, Permutation - Counting permutations, Permutation - Abstract algebra, Permutation - Notation, Permutation - More details, Permutation - Special permutations, Permutation - Permutations in computing, Permutation - Numbering permutations Read more here: » Permutation: Encyclopedia II - Permutation - Permutations in computing |
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| | | | iota: Encyclopedia II - Permutation - Special permutations If we think of a permutation that "changes" the position of the first element to the first element, the second to the second, and so on, we really have not changed the positions of the elements at all. Because of its action, we describe it as the identity permutation because it acts as an identity function.
If we have some permutation called P, we can describe a permutation, written P−1, which undoes the action of applying P. In essence, performing P then P−1 is the same as perform ...
See also:Permutation, Permutation - Arrangements and substitutions, Permutation - Counting permutations, Permutation - Abstract algebra, Permutation - Notation, Permutation - More details, Permutation - Special permutations, Permutation - Permutations in computing, Permutation - Numbering permutations Read more here: » Permutation: Encyclopedia II - Permutation - Special permutations |
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| | | | iota: Encyclopedia II - Trinity - Dissent from the doctrine Most Christians believe that the orthodox doctrine of the Trinity is so central to the Christian faith, that to deny it is to reject the Christian faith entirely. However a number of nontrinitarian groups, both throughout history and today, identify themselves as Christians but reject the doctrine of the Trinity in any form, arguing that theirs was the original pre-Nicean understanding. Some ancient sects, such as the Ebionites, said that Jesus was not a "Son of God", but rather an ordinary man who was a prophet. Many modern groups also teac ...
See also:Trinity, Trinity - Scripture and tradition, Trinity - Baptism as the beginning lesson, Trinity - Scriptural texts cited as implicit support for the doctrine of the Trinity, Trinity - Ontology of the Trinity, Trinity - Historical view and usage, Trinity - One God, Trinity - God exists in three persons, Trinity - Orthodox Roman Catholic and Protestant distinctions, Trinity - Historical development, Trinity - Dissent from the doctrine, Trinity - Other views of the Trinity, Trinity - Theory of pagan origin and influence, Trinity - Christian life and the Blessed Trinity, Trinity - Similarities in the 16th-century Jewish Kabbalah, Trinity - In popular culture Read more here: » Trinity: Encyclopedia II - Trinity - Dissent from the doctrine |
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More material related to Iota can be found here:
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