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Significations et usages de distinct
Définition
distinct (adj.)
1.distinctly separate from the first"that's another (or different) issue altogether"
2.clearly or sharply defined to the mind"clear-cut evidence of tampering" "Claudius was the first to invade Britain with distinct...intentions of conquest" "trenchant distinctions between right and wrong"
3.recognizable; marked"noticed a distinct improvement" "at a distinct (or decided) disadvantage"
4.easy to perceive; especially clearly outlined"a distinct flavor" "a distinct odor of turpentine" "a distinct outline" "the ship appeared as a distinct silhouette" "distinct fingerprints"
5.(often followed by `from') not alike; different in nature or quality"plants of several distinct types" "the word `nationalism' is used in at least two distinct senses" "gold is distinct from iron" "a tree related to but quite distinct from the E..."
6.constituting a separate entity or part"a government with three discrete divisions" "on two distinct occasions"
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Merriam Webster
DistinctDis*tinct" (?), a. [L. distinctus, p. p. of distinguere: cf. F. distinct. See Distinguish.]
1. Distinguished; having the difference marked; separated by a visible sign; marked out; specified. [Obs.]
Wherever thus created -- for no place
Is yet distinct by name. Milton.
2. Marked; variegated. [Obs.]
The which [place] was dight
With divers flowers distinct with rare delight. Spenser.
3. Separate in place; not conjunct; not united by growth or otherwise; -- with from.
The intention was that the two armies which marched out together should afterward be distinct. Clarendon.
4. Not identical; different; individual.
To offend, and judge, are distinct offices. Shak.
5. So separated as not to be confounded with any other thing; not liable to be misunderstood; not confused; well-defined; clear; as, we have a distinct or indistinct view of a prospect.
Relation more particular and distinct. Milton.
Syn. -- Separate; unconnected; disjoined; different; clear; plain; conspicuous; obvious.
DistinctDis*tinct" (?), v. t. To distinguish. [Obs.] Rom. of R.
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Définition (complément)
⇨ voir la définition de Wikipedia
Synonymes
distinct (adj.)
apparent, clean, clear, clear-cut, clearly perceptible, conspicuous, decided, definite, different, discrete, dissimilar, distinctly, distinguishable, divergent, graphic, lucid, manifest, marked, obvious, only, other, perfect, plain, separate, separated, sharp, special, trenchant, understandable, unlike, unmistakable, vivid, vividly
Voir aussi
distinct (adj.)
↘ apart, asunder, difference, differently, discretely, other than, otherwise, separately ↗ clearly, differ, differ about, differ from, differ in, differ on, differ over, differ with, dissent from, distinctly, diverge from, vary, vary from, vary in ≠ indistinct
Locutions
⇨ Distance of distinct vision • Distinct Nature • Distinct population segment • Distinct society • Distinct society clause • Distinct'ive Records • Least distance of distinct vision • Legal status of Jainism as a distinct religion in India • List of distinct cell types in the adult human body
Dictionnaire analogique
distinct (adj.)
distinct (adj.)
shrill[Classe]
sans mélange, à la perception claire, facile : net (fr)[Classe]
distinct (adj.)
clear[Similaire]
distinct (adj.)
definite[Similaire]
distinct (adj.)
distinctness, sharpness - clearly, distinctly - distinctly[Dérivé]
indistinct[Ant.]
distinct (adj.)
different[Similaire]
Wikipedia
Distinct
 |
This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (December 2009) |
Two or more things are distinct if no two of them are the same thing. In mathematics, two things are called distinct if they are not equal.
Example
A quadratic equation over the complex numbers sometimes has two roots.
The equation
factors as
and thus has as roots x = 1 and x = 2. Since 1 and 2 are not equal, these roots are distinct.
In contrast, the equation:
factors as
and thus has as roots x = 1 and x = 1. Since 1 and 1 are (of course) equal, the roots are not distinct; they coincide.
In other words, the first equation has distinct roots, while the second does not. (In the general theory, the discriminant is introduced to explain this.)
Proving distinctness
In order to prove that two things x and y are distinct, it often helps to find some property that one has but not the other. For a simple example, if for some reason we had any doubt that the roots 1 and 2 in the above example were distinct, then we might prove this by noting that 1 is an odd number while 2 is even. This would prove that 1 and 2 are distinct.
Along the same lines, one can prove that x and y are distinct by finding some function f and proving that f(x) and f(y) are distinct. This may seem like a simple idea, and it is, but many deep results in mathematics concern when you can prove distinctness by particular methods. For example,
- The Hahn–Banach theorem says (among other things) that distinct elements of a Banach space can be proved to be distinct using only linear functionals.
- In category theory, if f is a functor between categories C and D, then f always maps isomorphic objects to isomorphic objects. Thus, one way to show two objects of C are distinct (up to isomorphism) is to show that their images under f are distinct (i.e. not isomorphic).
See also
 |
Look up distinct in Wiktionary, the free dictionary. |
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