Definition talk:Boolean Algebra/Definition 2

Also see Definition talk:Boolean Algebra/Definition 1

inverses or identities

That latest change ... I still say this describes "inverses", although it's a compound rule: element product with complement equals an element which is an identity. Tricky to say exactly what this rule ought to be called. --prime mover (talk) 19:28, 16 October 2013 (UTC)

I see; it's a two-in-one type of thing. But you can't have inverses without identities, so I'm tempted to stick with that. — Lord_Farin (talk) 20:32, 16 October 2013 (UTC)

That's basically it. a) $a \wedge \neg a$ goes to make an element ($e$, whatever) which b) has the property that $e \vee b = b$.

But I point you towards Definition:Inverse Semigroup, where inverses are defined without there necessarily being an identity for them to be relative to.

And yes I know I posted it up without a source citation, and no I don't remember where from ... it may have been in one of the exercises out of 1965: Seth Warner: Modern Algebra but I can't find it now (and I have a nasty feeling it may even have come out of Wikipedia, oh the shame of it). --prime mover (talk) 06:59, 17 October 2013 (UTC)