Cantor Confusion
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From: David Marcus on 23 Jan 2007 14:04 G. Frege wrote: > On Tue, 23 Jan 2007 12:52:11 -0500, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > > > There is some perverse pleasure in winning an argument with someone even > > if the other person has no clue that you have won. And, the fact that > > you are winning is much clearer (at least to you and to intelligent > > bystanders) when arguing about math than when arguing about, say, > > politics. > > Hmmm... hmmm... I think the point (for me) is that *I* am interested > in the matters itself we are talking about (here). With other words, > when discussing a topic I am aiming for (the) truth, not for winning > an argument. (At least this is my "ideal".) A worthy ideal. > >> [...] Surely you will have noticed that there is (literally) NO progress > >> when arguing with WM. (Imho it's extremely nonsensical to "argue" with > >> such a guy.) > >> > > I basically agree, although whether it is extremely nonsensical depends > > on the goal. What do you suggest we do with cranks? Just ignore them? > > Basically, yes (I'd say). > > Torkel Franzen once wrote (in this NG): > > "[...] Wolfgang M�ckenheim is a classic crank. Why do you imagine, as > you seem to do, that there is any point arguing with him?" OK. If everyone else ignores him, I will too. However, if we (meaning people who understand math) are going to carry on a public discussion with him, I don't think it hurts if I toss in a few posts to help "our side". Nothing worse than having a public argument with a crank and have people who don't know much mathematics conclude that a real discussion is going on. In other words, if we publicly argue with a crank, we should win. -- David Marcus
From: David Marcus on 23 Jan 2007 14:04 G. Frege wrote: > On Tue, 23 Jan 2007 12:58:51 -0500, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > > > Why are you reading this thread? Is it sensible to do so? > > Well, actually I'm ONLY "reading" some answers to WM. After all, I > might learn something. (I'm still a beginner concerning set theory.) Sounds like a rationalization. :) -- David Marcus
From: imaginatorium on 23 Jan 2007 14:07 Andy Smith wrote: > stephen(a)nomail.com writes > >You still seem to be missing it. > > Maybe. The issue wasn't with a finite list, it was whether you could > have an infinite list when all the indices of the rows i.e. all natural > numbers, must be finite ... resolved by considering the list as "an > infinite set" just as the set of "all natural numbers" can be considered > as "an infinite set", even though no member of the natural numbers are > infinite; "an infinite set" is an abstract mental concept. > > If you see this as straightforward it is because your mindset has been > conditioned by your education to see this as normal. If you want to know what it feels like to be labelled a "crank", just start going on and on about mindsets being "conditioned". (If there is such a thing as "feeling" after your head has been bitten off.) Yeah, yeah, we have all memorised this stuff, which we mumble to ourselves at breakfast to make sure we don't forget... > If I was asked to sum it up, at present I would say that my > understanding is that you can't have an actually infinite integer, but > reals can be defined as having an actually infinite binary > representation .. (with apologies for the adjective "actually"). So no > surprise that the reals are "uncountable". And if you want to make progress, have respect for technical terms. "Uncountable" means something very specific. Does 1/7 have an "actually infinite binary representation" in your terms? Decimal fractions for "most" rational numbers go on without ending - but the rationals are not uncountable. Brian Chandler http://imaginatorium.org
From: David Marcus on 23 Jan 2007 14:09 G. Frege wrote: > On Tue, 23 Jan 2007 13:48:45 -0500, David Marcus > <DavidMarcus(a)alumdotmit.edu> wrote: > > >> It is impossible that the "whole" set of even numbers has a cardinal number > >> which is larger than every even number. > >> > > Why? > > Because WM thinks so. > > > F. > > P.S. > You couldn't resist. Right? ;-) I could, but can't I have some fun playing with the animals at the zoo? OK, time to do something useful with my day... -- David Marcus
From: G. Frege on 23 Jan 2007 14:08
On Tue, 23 Jan 2007 14:04:50 -0500, David Marcus <DavidMarcus(a)alumdotmit.edu> wrote: >>> >>> Why are you reading this thread? Is it sensible to do so? >>> >> Well, actually I'm ONLY "reading" some answers to WM. After all, I >> might learn something. (I'm still a beginner concerning set theory.) >> > Sounds like a rationalization. :) > Drinking problem? I don't have a drinking problem! I drink, fall down, stand up, drinking again. No drinking problem. F. -- E-mail: info<at>simple-line<dot>de |