1 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" [ant: indistinct]
2 (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 European beech"; "management had interests quite distinct from those of their employees" [syn: distinguishable]
3 constituting a separate entity or part; "a government with three discrete divisions"; "on two distinct occasions" [syn: discrete]
4 recognizable; marked; "noticed a distinct improvement"; "at a distinct (or decided) disadvantage" [syn: decided]
5 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" [syn: clear-cut, trenchant]
- Rhymes with: -ɪŋkt
different from one another
- ttbc Interlingua: distincte
- ttbc Spanish: distinto m, distinta f
- ttbc Telugu: విలక్షణమైన (vilakshaNamaina)
- SAMPA: /dis.tE~/
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.
- x2 − 3x + 2 = 0
- (x − 1)(x − 2) = 0
In contrast, the equation:
- x2 − 2x + 1 = 0
- (x − 1)(x − 1) = 0
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 distinctnessIn 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 (up to isomorphism).
distinct in German: Paarweise verschieden
distinct in Thai: ภาวะแตกต่าง
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