22/11/06 22:47:42.17 4rX/NHRo.net
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ｽﾚﾘﾝｸ(math板:604番)
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URLﾘﾝｸ(en.wikipedia.org)
In mathematics, the axiom of dependent choice, denoted by DC
Relation with other axioms
Unlike full AC, DC is insufficient to prove (given ZF) that there is a non-measurable set of real numbers
The axiom of dependent choice implies the axiom of countable choice and is strictly stronger.[4][5]
It is possible to generalize the axiom to produce transfinite sequences.
If these are allowed to be arbitrarily long, then it becomes equivalent to the full axiom of choice.
URLﾘﾝｸ(ja.wikipedia.org)
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