132 名前：d numbers, and the usual ordering applies within the evens and the odds: 0 2 4 6 8 ... 1 3 5 7 9 ... This is a well-ordered set of order type ω + ω. Every element has a successor (there is no largest element). Two elements lack a predecessor: 0 and 1.
Reals The standard ordering ≦ of any real interval is not a well ordering, since, for example, the open interval (0, 1) ⊆ [0,1] does not contain a least element. From the ZFC axioms of set theory (including the axiom of choice) one can show that there is a well order of the reals. Also Wac?aw Sierpi?ski proved that ZF + GCH (the generalized continuum hypothesis) imply the axiom of choice and hence a well order of the reals. Nonetheless, it is possible to show that the ZFC+GCH axioms alone are not sufficient to prove the existence of a definable (by a formula) well order of the reals.[1] However it is consistent with ZFC that a definable well ordering of the reals exists?for example, it is consistent with ZFC that V=L, and it follows from ZFC+V=L that a particular formula well orders the reals, or indeed any set.
