19/10/09 11:52:12.46 nHmzRvjt.net
>>216
つづき
・ω (omega) is defined as the lowest transfinite ordinal number and is the order type of the natural numbers under their usual linear ordering.
・Aleph-naught, アレフ_{0}, is defined as the first transfinite cardinal number and is the cardinality of the infinite set of the natural numbers. If the axiom of choice holds, the next higher cardinal number is aleph-one, アレフ_{1}.
If not, there may be other cardinals which are incomparable with aleph-one and larger than aleph-naught. But in any case, there are no cardinals between aleph-naught and aleph-one.
The continuum hypothesis states that there are no intermediate cardinal numbers between aleph-null and the cardinality of the continuum (the set of real numbers): that is to say, aleph-one is the cardinality of the set of real numbers. (If Zermelo?Fraenkel set theory (ZFC) is consistent, then neither the continuum hypothesis nor its negation can be proven from ZFC.)
(引用終り)
以上
注：「アレフ_{0}」などは、例のアレフ記号なのだが、文字化けするのです。Alephと書くと、記号でないAlephと区別できなので、カナ書きにした(゜ロ゜;。まあ、原文読んでください（＾＾