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Ad Infinitum
''Ad infinitum'' is a Latin phrase meaning "to infinity" or "forevermore". Description In context, it usually means "continue forever, without limit" and this can be used to describe a non-terminating process, a non-terminating ''repeating'' process, or a set of instructions to be repeated "forever," among other uses. It may also be used in a manner similar to the Latin phrase ''et cetera'' to denote written words or a concept that continues for a lengthy period beyond what is shown. Examples include: * "The sequence 1, 2, 3, ... continues ''ad infinitum''." * "The perimeter of a fractal may be iteratively drawn ''ad infinitum''." The 17th-century writer Jonathan Swift incorporated the idea of self-similarity in the following lines from his satirical poem ''On Poetry: a Rhapsody'' (1733): The vermin only teaze and pinch Their foes superior by an inch. So, naturalists observe, a flea Has smaller fleas that on him prey; And these have smaller still to bite 'em, And so proceed ''ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the Roman Republic it became the dominant language in the Italian region and subsequently throughout the Roman Empire. Even after the fall of Western Rome, Latin remained the common language of international communication, science, scholarship and academia in Europe until well into the 18th century, when other regional vernaculars (including its own descendants, the Romance languages) supplanted it in common academic and political usage, and it eventually became a dead language in the modern linguistic definition. Latin is a highly inflected language, with three distinct genders (masculine, feminine, and neuter), six or seven noun cases (nominative, accusative, genitive, dative, ablative, and vocative), five declensions, four verb conjuga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Siphonaptera (poem)
"Siphonaptera" is a name usedFor example: to refer to the following rhyme by Augustus De Morgan (''Siphonaptera'' being the biological order to which fleas belong): The rhyme appears in De Morgan's ''A Budget of Paradoxes'' (1872) along with a discussion of the possibility that all particles may be made up of clusters of smaller particles, 'and so down, for ever'; and similarly that planets and stars may be particles of some larger universe, 'and so up, for ever'. The lines derive from part of Jonathan Swift's long satirical poem "On Poetry: A Rapsody" of 1733: Lewis F. Richardson adapted the poem to meteorology in 1922: See also *Self-similarity __NOTOC__ In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically se ... * Turtles all the way down References {{DEFAULTSORT:Siphonaptera English ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Song That Never Ends
"The Song That Doesn't End" (also referred to as "The Song That Never Ends") is a self-referential and infinitely iterative children's song. The song appears in an album by puppeteer Shari Lewis titled '' Lamb Chop's Sing-Along, Play-Along'', released through a 1988 home video. It is a single-verse-long song, written in an infinite-loop motif in a march style, such that it naturally flows in a cyclical fashion, repeating the same verse over and over. It is still a very popular tune, typically sung during long car rides. The song was written by Shari Lewis' long time producer Bernard Rothman. Lyrics (The song repeats endlessly.) Variations Alternative versions of the song use "never ends". Other minor discrepancies in the lyrics may be due to the song being passed in the oral tradition from kid-to-kid. Such differences include "It just goes on and on..." (line 2), "And we’ll continue" (line 4) and " and they continued" (line 4) Notable appearances and recordings A versio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-reference
Self-reference occurs in natural or formal languages when a sentence, idea or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding. In philosophy, it also refers to the ability of a subject to speak of or refer to itself, that is, to have the kind of thought expressed by the first person nominative singular pronoun "I" in English. Self-reference is studied and has applications in mathematics, philosophy, computer programming, second-order cybernetics, and linguistics, as well as in humor. Self-referential statements are sometimes paradoxical, and can also be considered recursive. In logic, mathematics and computing In classical philosophy, paradoxes were created by self-referential concepts such as the omnipotence paradox of asking if it was possible for a being to exist so powerful that it could create a stone that it could not lift. The Epimenides paradox, 'All Cretans are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursion
Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references ("crock recursion") can occur. Formal definitions In mathematics and computer science, a class of objects or methods exhibits recursive behavior when it can be defined by two properties: * A simple ''base case'' (or cases) — a terminating scenario that does not use recursion to produce an answer * A ''recursive step'' — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ''ancestor''. One's ances ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Induction
Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for ''n'' = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case ''n'' = ''k'', ''then'' it must also hold for the next case ''n'' = ''k'' + 1. These two steps establish that the statement holds for every natural number ''n''. The base case does not necessarily begin with ''n'' = 0, but often with ''n'' = 1, and possibly with any fixed natural number ''n'' = ''N'', establishing the truth of the statement for all natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Latin Phrases
__NOTOC__ This is a list of Wikipedia articles of Latin phrases and their translation into English. ''To view all phrases on a single, lengthy document, see: List of Latin phrases (full)'' The list also is divided alphabetically into twenty pages: * List of Latin phrases (A) * List of Latin phrases (B) * List of Latin phrases (C) * List of Latin phrases (D) * List of Latin phrases (E) * List of Latin phrases (F) * List of Latin phrases (G) * List of Latin phrases (H) * List of Latin phrases (I) * List of Latin phrases (L) * List of Latin phrases (M) * List of Latin phrases (N) * List of Latin phrases (O) * List of Latin phrases (P) * List of Latin phrases (Q) * List of Latin phrases (R) * List of Latin phrases (S) * List of Latin phrases (T) * List of Latin phrases (U) * List of Latin phrases (V) See also * Latin influence in English * Latinism Lists *List of abbreviations used in medical prescriptions *List of ecclesiastical abbreviations *List of Germanic a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-similarity
__NOTOC__ In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant; it can be continually magnified 3x without changing shape. The non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed. A time developing phenomenon is said to exhibit self-similarity if the numerical v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jonathan Swift
Jonathan Swift (30 November 1667 – 19 October 1745) was an Anglo-Irish Satire, satirist, author, essayist, political pamphleteer (first for the Whig (British political party), Whigs, then for the Tories (British political party), Tories), poet, and Anglican cleric who became Dean (Christianity), Dean of St Patrick's Cathedral, Dublin, hence his common sobriquet, "Dean Swift". Swift is remembered for works such as ''A Tale of a Tub'' (1704), ''An Argument Against Abolishing Christianity'' (1712), ''Gulliver's Travels'' (1726), and ''A Modest Proposal'' (1729). He is regarded by the ''Encyclopædia Britannica'' as the foremost prose satirist in the English language, and is less well known for his poetry. He originally published all of his works under pseudonyms—such as Lemuel Gulliver, Isaac Bickerstaff, M. B. Drapier—or anonymously. He was a master of two styles of satire, the Satire#Classifications, Horatian and Juvenalian styles. His deadpan, ironic writing style, partic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
