On Oct 10, 12:30 am, Jim Greenfield <jgreenfiel...@gmail.com> wrote: > On Oct 7, 1:04 am, PD <thedraperfam...@gmail.com> wrote: > > > > > > > > > > > On 10/5/2011 9:30 PM, Transfer Principle wrote: > > > > On Oct 5, 7:30 am, PD<thedraperfam...@gmail.com> wrote: > > >> On 10/5/2011 4:27 AM, Alen wrote: > > >>> GENERAL DEFINITION OF AN INFINITY !! TA DA !! :) > > >>> An infinity is a reality which forms a basis that > > >>> enables the existence of the finite, the countable > > >>> or measurable, but is not in itself either countable or > > >>> measurable. > > >> Alen, allow me to make a general and hopefully polite observation. > > >> I'm all for people rethinking things from scratch. However, you can do > > >> this two ways. One is after taking the trouble to see what others have > > >> done already, and the other is without bothering to see what others have > > >> done. > > > > But if one doesn't have _access_ to what others have done already, > > > then the second option is the only available option. And, as we've > > > already seen from earlier threads, ZFC mainly considers _books_, > > > not the Internet (especially not Wikipedia), to be legitimate > > > sources of what others have done. So if one doesn't have access to > > > those _books_, the second option is the only available option. > > > >> I also think that those people WANT to think that both are just as good, > > >> because the second is definitely easier. > > > > Not only is the second easier, but the first might be _impossible_, > > > for those who don't have access to the right books. > > > But you DO have access to books. I'll remind you that students are not > > wealthy. Many of them live on stipends well below the poverty level and > > they STILL devote a dominant part of their investment to those things > > that are important to them, including books. > > > Now, what may be true for hobbyists is that they only WANT to apply a > > personal investment at the hobby level, and THAT low level of personal > > investment prohibits them from getting access to the books and materials > > that more serious students gain. > > > I believe the complaint then is that some hobbyists either want the SAME > > level of access to materials that more serious researchers have but at > > no cost, or they want to be excused for choosing to avail themselves of > > only the internet and still hope to make significant progress. > > > I'm sorry, but that's not a practical option. It just isn't. > > > >> This, frankly, is a fabricated excuse for laziness. > > > > Lazy just because one can't make books materialize out of thin air? > > > >> It also borders on hubris, because the implicit claim is that one can > > >> get *just* as far by rethinking from scratch, without having bothered to > > >> see what others have already done. > > > > The implicit claim is that everyone has access to the same books as > > > you do. > > > >> The other excuse is an unjustified terror that one simply cannot rethink > > >> from scratch after taking the trouble to see what others have done > > >> already, because one's mind has become so contaminated that it can't > > >> rethink from scratch. > > > > My own excuse is the _justified_ terror that one simply might not have > > > access to the right books. > > > > Now who knows? Perhaps the OP really does have access to the right > > > books, and can really learn more about infinity. If so, then PD's post > > > will be helpful to the OP. Let me add a warning to the OP, though, > > > that > > > some books are "right" while others are wrong. I've mentioned in some > > > earlier threads that the "wrong" books are those popular expositions > > > which make basic mistakes, such as _defining_ aleph_1 as 2^aleph_0. > > > The > > > "right" books are the ones that look like _textbooks_. > > > This is absolutely right. Caveat emptor. There are lots of hobbyists who > > say things like, "I DO have books. I've read A Brief History of Time > > twice." This, of course, is simply a case of squandering money > > foolishly. A man who wants to learn how to be a car mechanic isn't going > > to buy his tools at Dollar General. > > A really good mechanic can do a good job with a hammer, pliers, > screwdriver > > Jim G > 1/0 = oo >
Just keep telling yourself that you're a really good physicist and so you don't need fancy tools.
