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In mathematics, a binary relation ''R'' over a set ''X'' is total or complete if for all ''a'' and ''b'' in ''X'', ''a'' is related to ''b'' or ''b'' is related to ''a'' (or both). In mathematical notation, this is : Total relations are sometimes said to have ''comparability''. == Examples == For example, "is less than or equal to" is a total relation over the set of real numbers, because for two numbers either the first is less than or equal to the second, or the second is less than or equal to the first. On the other hand, "is less than" is not a total relation, since one can pick two equal numbers, and then neither the first is less than the second, nor is the second less than the first. (But note that "is less than" is a weak order which gives rise to a total order, namely "is less than or equal to". The relationship between strict orders and weak orders is discussed at partially ordered set.) The relation "is a subset of" is also not total because, for example, neither of the sets and is a subset of the other. 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「Total relation」の詳細全文を読む スポンサード リンク
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