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nonsymmetrical
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Possible Dictionary Clues |
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Not symmetrical. |
Nonsymmetrical might refer to |
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In mathematics, an Asymmetric relation is a binary relation on a set X where:* For all a and b in X, if a is related to b, then b is not related to a.In mathematical notation, this is: * * * * * ∀ * a * , * b * ∈ * X * ( * a * R * b * ⇒ * ¬ * ( * b * R * a * ) * ) * * * {\displaystyle \forall a,b\in X(aRb\Rightarrow \lnot (bRa))} * An example is the "less than" relation < between real numbers: if x < y, then necessarily y is not less than x.The "less than or equal" relation ≤, on the other hand, is not asymmetric, because reversing e.g. x ≤ x produces x ≤ x and both are true. In general, any relation in which x R x holds for some x (that is, which is not irreflexive) is also not asymmetric. * Asymmetry is not the same thing as "not symmetric": the less-than-or-equal relation is an example of a relation that is neither symmetric nor asymmetric. The empty relation is the only relation that is (vacuously) both symmetric and asymmetric. |