Talk:Abstract Algebra/Group Theory/Group

Isn't Theorem 17 valid only for finite groups? --92.251.213.252 (discuss) 20:30, 22 November 2014 (UTC)

It may be worth discussing whether a more constructive definitional style is appropriate. For example, a monoid is defined as a set M with operation * which is associative and for which "there exists an element e" acting as an identity.

A more constructive approach would require specifying the element e in M as part of the specification data. This would indeed be essential from a computing viewpoint. It is also essential for more complex structures where the mere existence of some element or structure is not enough to fix which structure is under consideration, in the event the element or structure is not unique.