Ordinal Numbers: Bridging English & Set Theory

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dalcde
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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.
 

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dalcde said:
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.

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
 
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dalcde said:
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.
Yes, a cardinal describes the size of a set, an ordinal describes the position of an element in a series.
 

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