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Ordinal Number

  1. Sep 15, 2011 #1
    How are ordinal numbers in set theory/order theory related to ordinal numbers in English? There should somehow be a bit of relationship for them to share the same name.
  2. jcsd
  3. Sep 15, 2011 #2
    The common usage refers to the natural order of the non-negative integers in terms of the [itex]k[/itex]th integer. In set theory a finite well ordered set has a least element and an order type corresponding to its cardinality [itex]k[/itex]. A totally ordered finite set is a well ordered set whose elements are ordered corresponding to the natural order of the non-negative integers
    Last edited: Sep 15, 2011
  4. Sep 15, 2011 #3
    Yes, a cardinal describes the size of a set, an ordinal describes the position of an element in a series.
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