Recent content by airpocket

Thanks so much. That makes sense. I didn't think about simplifying x + y.

The sum of two subspaces seems a simple enough concept to me, but I must be misunderstanding it since I don't understand why Axler gives an answer he does in Linear Algebra Done Right. Suppose U and W are subspaces of some vector space V. U = \{(x, 0, 0) \in \textbf{F}^3 : x \in...

Yeah, closure as an explicit axiom does make it sound like a much better match to me, so that's probably it if you've seen it mentioned like that as an axiom. You've convinced me. Thanks again for your help.

Thanks for the reply. You labeled your points 1 to 4 but you could just as easily split set and binary operation on the set into 2 separate points and then you'd have 1 through 5 (and semigroup=3, group=5). And that doesn't change the fact that the standard formulation is 1 property for a...

This is a stupid question, but perhaps somebody else has had the same stupid question before and found an answer. Why is a <b>semi</b>group so named? If a group were a set and a binary operation satisfying 2 additional properties, then semigroup would be the perfect name, since it satisfies...