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trivial

Did you mean: trivial, Trivial (Traditional iPhone Game), Trivial (2007 Thriller Film)

 
Dictionary: triv·i·al   (trĭv'ē-əl) pronunciation
adj.
  1. Of little significance or value.
  2. Ordinary; commonplace.
  3. Concerned with or involving trivia.
  4. Biology. Relating to or designating a species; specific.
  5. Mathematics.
    1. Of, relating to, or being the solution of an equation in which every variable is equal to zero.
    2. Of, relating to, or being the simplest possible case; self-evident.

[Middle English trivialle, of the trivium (from Medieval Latin triviālis , from trivium, trivium; see trivium) and Latin triviālis, ordinary (from trivium, crossroads).]

trivially triv'i·al·ly adv.

SYNONYMS   trivial, trifling, paltry, petty, picayune. These adjectives all apply to what is small and unimportant. Trivial and trifling refer to what is so insignificant as to be utterly commonplace or unremarkable: "I think all Christians . . . agree in the essential articles, and that their differences are trivial" (Samuel Johnson). "I regret the trifling narrow contracted education of the females of my own country" (Abigail Adams). Paltry describes what falls so far short of what is required or desired that it arouses contempt: "He . . . considered the prize too paltry for the lives it must cost" (John Lothrop Motley). Petty can refer to what is of minor or secondary significance or size: "Our knights are limited to petty enterprises" (Sir Walter Scott). What is picayune is of negligible value or importance: a picayune infraction of the law.

WORD HISTORY   The word trivial entered Middle English with senses quite different from its most common contemporary ones. We find in a work from 1432-50 mention of the "arte trivialle," an allusion to the three liberal arts that made up the trivium, the lower division of the seven liberal arts taught in medieval universities-grammar, rhetoric, and logic. The history of trivial goes back to the Latin word trivium, formed from the prefix tri-, "three," and via, "road." Trivium thus meant "the meeting place of three roads, especially as a place of public resort." The publicness of such a place also gave the word a pejorative sense that we express in the phrase the gutter, as in "His manners were formed in the gutter." The Latin adjective triviālis, derived from trivium, thus meant "appropriate to the street corner, commonplace, vulgar." Trivial is first recorded in English with a sense identical to that of triviālis in 1589. Shortly after that trivial is recorded in the sense most familiar to us, "of little importance or significance," making it a word now used of things less weighty than grammar, rhetoric, and logic.


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Antonyms: trivial
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adj

Definition: not important
Antonyms: consequential, important, significant, useful, valuable, weighty, worthwhile


Hacker Slang: trivial
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1. Too simple to bother detailing.

2. Not worth the speaker's time.

3. Complex, but solvable by methods so well known that anyone not utterly cretinous would have thought of them already.

4. Any problem one has already solved (some claim that hackish trivial usually evaluates to “I've seen it before”). Hackers' notions of triviality may be quite at variance with those of non-hackers. See nontrivial, uninteresting.

The physicist Richard Feynman, who had the hacker nature to an amazing degree (see his essay “Los Alamos From Below” in Surely You're Joking, Mr. Feynman!), defined trivial theorem as “one that has already been proved”.


Word Tutor: trivial
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pronunciation

IN BRIEF: Small and of little importance. Also: Obvious and dull.

pronunciation The difference between what the most and the least learned people know is inexpressibly trivial in relation to that which is unknown. — Albert Einstein (1879-1955)

Wikipedia: Trivial (mathematics)
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In mathematics, the adjective trivial is frequently used for objects (for examples, groups or topological spaces) that have a very simple structure. The noun triviality usually refers to a simple technical aspect of some proof or definition.

Trivial objects or structures

For non-mathematicians, they are sometimes more difficult to visualize or understand than other, more complicated objects.

Examples include:

Trivial also refers to solutions to an equation that have a very simple structure, but for the sake of completeness cannot be omitted. These solutions are called the trivial solution. For example, consider the differential equation

y' = y

where y = f(x) is a function whose derivative is y′. The trivial solution is

y = 0, the zero function

while a nontrivial solution is

y (x) = ex, the exponential function.

Similarly, mathematicians often describe Fermat's Last Theorem as asserting that there are no nontrivial solutions to the equation an + bn = cn when n is greater than 2. Clearly, there are some solutions to the equation. For example, a = b = c = 0 is a solution for any n, as is a = 1, b = 0, c = 1. But such solutions are all obvious and uninteresting, and hence "trivial".

Triviality in mathematical reasoning

Trivial may also refer to any easy case of a proof, which for the sake of completeness cannot be ignored. For instance, proofs by mathematical induction have two parts: the "base case" that shows that the theorem is true for a particular initial value such as n=0 or n = 1 and then an inductive step that shows that if the theorem is true for a certain value of n, it is also true for the value n+1. The base case is often trivial and is identified as such, although there are cases where the base case is difficult but the inductive step is trivial. Similarly, one might want to prove that some property is possessed by all the members of a certain set. The main part of the proof will consider the case of a nonempty set, and examine the members in detail; in the case where the set is empty, the property is trivially possessed by all the members, since there are none. (See also Vacuous truth.)

A common joke in the mathematical community is to say that "trivial" is synonymous with "proved" — that is, any theorem can be considered "trivial" once it is known to be true. Another joke concerns two mathematicians who are discussing a theorem; the first mathematician says that the theorem is "trivial". In response to the other's request for an explanation, he then proceeds with twenty minutes of exposition. At the end of the explanation, the second mathematician agrees that the theorem is trivial. These jokes point out the subjectivity of judgments about triviality. Someone experienced in calculus, for example, would consider the theorem that

\int_0^1 x^2\, dx = 1/3

to be trivial. To a beginning student of calculus, though, this may not be obvious at all.

Note that triviality also depends on context. A proof in functional analysis would probably, given a number, trivially assume the existence of a larger number. When proving basic results about the natural numbers in elementary number theory though, the proof may very well hinge on the remark that any natural number has a successor (which should then in itself be proved or taken as an axiom, see Peano's axioms).

See also


Translations: Trivial
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Dansk (Danish)
adj. - triviel, ubetydelig, ligegyldig, overfladisk

Nederlands (Dutch)
triviaal, alledaags

Français (French)
adj. - insignifiant, léger, trivial, futile

Deutsch (German)
adj. - trivial, banal, nichtssagend, unbedeutend, volkstümlich

Ελληνική (Greek)
adj. - κοινότοπος, τετριμμένος, ασήμαντος, επουσιώδης, επιπόλαιος, ελαφρός

Italiano (Italian)
triviale

Português (Portuguese)
adj. - insignificante, fútil, superficial, popular

Русский (Russian)
незначительный

Español (Spanish)
adj. - trivial, banal, insignificante, frívolo

Svenska (Swedish)
adj. - trivial, bagetallartad, oviktig, betydelselös, banal

中文(简体)(Chinese (Simplified))
琐细的, 微不足道的, 价值不高的

中文(繁體)(Chinese (Traditional))
adj. - 瑣細的, 微不足道的, 價值不高的

한국어 (Korean)
adj. - 하찮은, 진부한

日本語 (Japanese)
adj. - つまらない, 平凡な

العربيه (Arabic)
‏(صفه) تافه, عادي, مبتذل‏

עברית (Hebrew)
adj. - ‮קל-ערך, פעוט, חסר-חשיבות, מבוטל, רגיל, שגרתי, פשוט, שטחי‬


Best of the Web: trivial
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Some good "trivial" pages on the web:


Math
mathworld.wolfram.com
 
 
 

Did you mean: trivial, Trivial (Traditional iPhone Game), Trivial (2007 Thriller Film)

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