ऑर्डिनल्स इसके अंग्रेजी अर्थ का उदाहरण

As ordinals are well-ordered, this immediately implies the existence of a Hartogs number for any set X.

Now, because a transitive set of ordinals is again an ordinal, α is an ordinal.

In 1915, Hartogs could use neither von Neumann-ordinals nor the replacement axiom, and so his result is one of Zermelo set theory and looks rather different from the modern exposition above.

Von Neumann definition of ordinals "mdash; another way to encode natural numbers: as sets.

(Roughly speaking, the class of all ordinals in ZFC is an inaccessible cardinal apart from the fact that it is not a set, and the reflection principle can then be used to show that there is a set which has the same property, in other words which is an inaccessible cardinal.

In particular he is known for having calculated the values of all the projective ordinals (the suprema of the lengths of all prewellorderings of the real numbers at a particular level in the projective hierarchy) under the assumption that the axiom of determinacy holds.

The space of all ordinals at most equal to the first uncountable ordinal Ω, with the topology generated by open intervals, is a compact Hausdorff space.

The measure that assigns measure 1 to Borel sets containing an unbounded closed subset of the countable ordinals and assigns 0 to other Borel sets is a Borel probability measure that is neither inner regular nor outer regular.

Despite receiving four first place ordinals in the free dance, a strange ordinal situation caused them to place third in the free dance and drop from first to third in the end.

They seemed to be threatening for victory at the Worlds, with three first place ordinals ahead of Klimova " Ponomarenko in the original dance, but a fall in the free dance ended any hopes.

This was a commanding victory as they won all four phases of the competition at both events, and received straight first place ordinals, apart from losing two first place ordinals to the up-and-coming Russians Anjelika Krylova " Vladimir Fedorov at Worlds.

However the free dance of Grishuk " Platov which handily won that phase changed the ordinals, and Usova " Zhulin were pushed to third in the free dance behind Torvill " Dean and dropped to third overall.

Despite a better overall set of ordinals in the free dance than Grishuk " Platov with three first and six seconds to five firsts, one second, and three thirds for Grishuk " Platov, they lost gold by the majority rule, Grishuk " Platov having the five first place ordinals they needed to win the free dance.