# Ordinal Number

1. Sep 15, 2011

### dalcde

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. Sep 15, 2011

### SW VandeCarr

The common usage refers to the natural order of the non-negative integers in terms of the $k$th integer. In set theory a finite well ordered set has a least element and an order type corresponding to its cardinality $k$. 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
3. Sep 15, 2011

### Preno

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