A mostly unrelated notion from group theory is the cardinality of the underlying set of a group, especially when this is finite. Sometimes one thinks of an infinite group as having order zero. The orders then have the natural order relation of divisibility?.

The term ‘order’ can also be used fairly generically as a synonym of ‘degree’ or ‘rank’, as in first-order logic, the order of a differential equation, etc. Of course, these various orders form a well-order, so this is not entirely unrelated either.

Revised on October 17, 2012 12:51:20
by Urs Schreiber
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