Man most of the time I read mathematical proofs, I am stumpled on how to to prove them myself. Then after reading them, they often makes sence. Although I am able to do some of the simpler ones. I just feel discouraged, because I feel that I would have never discovered this or that =(
@tb Are you sure? I'm asking this question because in the definition for closed operator in my lecture notes it says "Let T be a linear operator from a normed linear space X into a normed vector space Y ..."
@Matt No problem :) These things happen (using two words for the same thing) in lectures or in notes, although one should try to avoid that. It is really confusing for people unacquainted with the subject and I understand your question and double-checking fully.
@TheChaz I am mainly skeptical that someone would've seriously used more than 1-2 introductory books on any topic. [To all: Please correct me if I am wrong.]
I actually asked it here math.stackexchange.com/questions/90536/… and I understood his answer, it's just I'm not sure my comments on his answer are correct and how to generalize it
I had the caps going well for a few months, but then I got out of larval stage, I suppose. Still 12 caps from Epic, and who knows how long it will take me to collect them at this pace ...
@HenningMakholm Well, I plan on getting to the 20k and becoming a trusted user and then define a notion of forcing called "Bully Forcing". The conditions are composed of the statement: "Why are you hitting yourself??"
I feel that deep within the knowledge of many users here dwell great problems regarding clever tricks for simplifying problems, and factoring algebraic expressions. I would be very much interested in seeing a large list of problems, regarding such problems.
Any problem that is clever, has somet...
Just figured out that I have to reread 1½ chapters of Kunen because I arrogantly figured that because I know NBG I could skip all of the nitty-gritty part about proper classes actually being abbreviations blah blah blah.
Then it suddenly dawned upon me that if I were to do a parallel development for NBG I would have to speak of collections of proper classes anyway in order to have, say, V as an inner model, so all of the nitty-gritty would be relevant anyway.
Since NBG is a conservative extension of ZFC, every proof in NBG which only uses sets can be written as a proof in ZFC. However if we consider class forcing in NBG the treatment is much easier than it is in ZFC; but when can a notion of forcing be adapted to such proof?
@tb Quite.
Well. In the remaining 20 minutes I guess you're all just gonna have to upvote my older questions, since no one asked an AC related question :-P
I'll have to chase down the proof that NBG extends ZF conservatively one of these days. Kunen makes a good point (as far as he makes it) that the ZF axioms are better intuitively motivated than the sweeping class existence axioms of NBG.