Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online lexicon:

Indirect Proof

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview
In order to show that a premise $ V$ implies an assertion $ B$ ( $ V \Longrightarrow B$), one can deduce a contradiction by assuming that $ V$ is true while $ B$ is false, which then implies a false statement $ F$, particularly with $ F = \lnot V$ or $ F=B$:

$\displaystyle V\land(\lnot B)\,\Longrightarrow\,F \,, $

In particular, we note that the equivalences

$\displaystyle B = (\lnot B \Longrightarrow F) \,=\,(\lnot B\Rightarrow B) $

hold if no premises are made.
(Authors: Höllig/Knesch/Apprich/Abele)

see also:

[Annotations] [Examples]
  automatically generated 9/18/2007