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Intransitivity
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Intransitivity : ウィキペディア英語版
Intransitivity

In mathematics, intransitivity (sometimes called nontransitivity) is a property of binary relations that are not transitive relations. This may include any relation that is not transitive, or the stronger property of antitransitivity, which describes a relation that is never transitive.
== Intransitivity ==

A relation is transitive if, whenever it relates some A to some B, and that B to some C, it also relates that A to that C. Some authors call a relation ''intransitive'' if it is not transitive, i.e. (if the relation in question is named R)
:\lnot\left(\forall a, b, c: a R b \land b R c \Rightarrow a R c\right).
This statement is equivalent to
: \exists a,b,c : a R b \land b R c \land \lnot(a R c)
For instance, in the food chain, wolves feed on deer, and deer feed on grass, but wolves do not feed on grass.〔Wolves do ''eat'' grass - see .〕 Thus, the ''feed on'' relation among life forms is intransitive, in this sense.
Another example that does not involve preference loops arises in freemasonry: it may be the case that lodge A recognizes lodge B, and lodge B recognizes lodge C, but lodge A does not recognize lodge C. Thus the recognition relation among Masonic lodges is intransitive.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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