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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 ) : This statement is equivalent to : 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）』 ■ウィキペディアで「intransitivity」の詳細全文を読む スポンサード リンク
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