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Distinct aus Wikipedia. Zum Beitrag

Distinct - Wikipedia, the free encyclopedia a:lang(ar),a:lang(ckb),a:lang(fa),a:lang(kk-arab),a:lang(mzn),a:lang(ps),a:lang(ur){text-decoration:none}a.new,#quickbar a.new{color:#ba0000} /* cache key: enwiki:resourceloader:filter:minify-css:4:c88e2bcd56513749bec09a7e29cb3ffa */ Distinct From Wikipedia, the free encyclopedia Jump to: , 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 x2 ? 3x + 2 = 0 factors as (x ? 1)(x ? 2) = 0 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: x2 ? 2x + 1 = 0 factors as (x ? 1)(x ? 1) = 0 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 mehr

Distinct aus Wikipedia. Zum Beitrag