Wed, 07 Aug 2019
Technical devices for reducing the number of axioms
In a recent article, I wrote:
There was a sub-digression, which I removed, about a similar sort of device that does have practical value. Suppose you have a group !!\langle G, \ast \rangle!! with a nonempty subset !!H\subset G!!, and you want to show that !!\langle H, \ast \rangle!! is a subgroup of !!G!!. To do this is it is sufficient to show three things:
Often, however, it is more convenient to show instead:
which takes care of all three at once.
[Other articles in category /math] permanent link