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What are ordinals?

What are ordinals? Here are some definitions.

Noun
  1. plural of ordinal
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Other monarchies assign ordinals to monarchs even if they are the only ones of their name.
In this latter book she presented a 30 page appendix on the theory of infinite cardinals and ordinals.
In Sweden, the practice is not consistent, as Sigismund and Adolf Frederick never have ordinals, whereas Frederick I often does.
Ordinals for monarchs before the 13th century are anachronisms, as are also ordinals for almost all later medieval monarchs.
In 1907 he introduced special types of ordinals in an attempt to prove Cantor's continuum hypothesis.
Having solved the open problem posed by Davenport on writing numbers as the sums of fifth powers, Conway began to become interested in infinite ordinals.

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