The inverses Halmos defines here are more general than the inverse functions described on wikipedia. Halmos' inverses work even when the functions are not bijective.
I believe that what you are speaking of here is Halmos's discourse on what are called these days "images and preimages" or "inverse images". I found the subtle difference between these and inverse functions proper annoying when I was learning proof writing, so let me illustrate the concept, so that we have a caveat emptor for the budding mathematician.
Take the se...
I used your axiom list and Zorn's lemma proof sketch to make Mnemosyne cards. Thanks a bunch!
Thanks, habryka. I added a short explanation and linked this in the post. I thought it would be more common knowledge than it is around these parts.
Nice dude!
I don't think this refutes my essential point, but it does add a caveat to it that might help exceptions realize when such a course wouldn't actually help them much. I've never taken a course in logic, and have in fact only recently cracked open a book on FOL proper.
I quite like this approach. :) I’ll see if I can apply it to electrical engineering and pure mathematics soon, as those are the subjects I am studying in school. Linear algebra will be my first stop.