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单词 NecessaryAndSufficient
释义

necessary and sufficient


The statement “p is necessary for q” “q implies (http://planetmath.org/ImplicationMathworldPlanetmath) p”.

The statement “p is sufficient for q” “p implies (http://planetmath.org/Implication) q”.

The statement “p is necessary and sufficent for q” “p if and only if (http://planetmath.org/Iff) q”.

For an example of how these terms are used in mathematics, see the entry on complete ultrametric fields.

BiconditionalMathworldPlanetmathPlanetmath statements are often proven by breaking them into two implications and proving them separately. Often, the terms necessity and sufficiency are used to indicate which implication is being proven. For an example of this usage, see the entry called relationship between totatives and divisors.

Titlenecessary and sufficient
Canonical nameNecessaryAndSufficient
Date of creation2013-03-22 16:07:31
Last modified on2013-03-22 16:07:31
OwnerWkbj79 (1863)
Last modified byWkbj79 (1863)
Numerical id12
AuthorWkbj79 (1863)
Entry typeDefinition
Classificationmsc 03B05
Classificationmsc 03F07
Related topicUniversalAssumption
Related topicSufficientConditionOfPolynomialCongruence
Definesnecessary
Definesnecessity
Definessufficient
Definessufficiency
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