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In mathematics, any two elements ''x'' and ''y'' of a set ''P'' that is partially ordered by a binary relation ≤ are comparable when either ''x'' ≤ ''y'' or ''y'' ≤ ''x''. If it is not the case that ''x'' and ''y'' are comparable, then they are called incomparable. A totally ordered set is exactly a partially ordered set in which every pair of elements is comparable. It follows immediately from the definitions of ''comparability'' and ''incomparability'' that both relations are symmetric, that is ''x'' is comparable to ''y'' if and only if ''y'' is comparable to ''x'', and likewise for incomparability. ==Notation== Comparability is denoted by the symbol ⊥, and incomparability by the symbol ||. Thus, for any pair of elements ''x'' and ''y'' of a partially ordered set, exactly one of * ''x'' ⊥ ''y'' and * ''x'' || ''y'' is true. 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「Comparability」の詳細全文を読む スポンサード リンク
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