|
In set theory, a set ''A'' is transitive, if and only if * whenever ''x'' ∈ ''A'', and ''y'' ∈ ''x'', then ''y'' ∈ ''A'', or, equivalently, * whenever ''x'' ∈ ''A'', and ''x'' is not an urelement, then ''x'' is a subset of ''A''. Similarly, a class ''M'' is transitive if every element of ''M'' is a subset of ''M''. == Examples == Using the definition of ordinal numbers suggested by John von Neumann, ordinal numbers are defined as hereditarily transitive sets: an ordinal number is a transitive set whose members are also transitive (and thus ordinals). Any of the stages ''V''α and ''L''''α'' leading to the construction of the von Neumann universe ''V'' and Gödel's constructible universe ''L'' are transitive sets. The universes ''L'' and ''V'' themselves are transitive classes. 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「transitive set」の詳細全文を読む スポンサード リンク
|