Obections to Cantor's Theory (Wikipedia article)
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From: malbrain on 28 Jul 2005 12:35 Virgil wrote: > In article <MPG.1d51c6ff1e95e695989fd7(a)newsstand.cit.cornell.edu>, > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > > > You folks are hopeless. > > We do not need your sick kind of hope when we have our healthy kind of > logic and correctness. Hope is not subject to disease. karl m
From: malbrain on 28 Jul 2005 12:41 Virgil wrote: > In article <MPG.1d51c8215386c4f2989fd9(a)newsstand.cit.cornell.edu>, > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > > > Daryl McCullough said: > > > Tony Orlow (aeo6) wrote: > > > > > > >Robert Low said: > > > > > > > >> OK, so how many elements are there in the set of all finite > > > >> natural numbers? > > > >> > > > >Some finite, indeterminate number. You tell me the largest finite > > > >number, and that's the set size. > > > > > > So you really think that there is some number n such that n is > > > finite, but if you add 1 you get an infinite number? > > (sigh) This is the last time I answer this question > > NOOOOOOOOOOO!!!!!!!!! > > But since every natural has an immediate successor, and except for the > first. an immediate predecessor, and there are no gaps( at least if one > accepts Peano), the only way of getting from finite to infinite is by > adding 1 to some finite natural to get an infinite natural. > > > > Maybe it's 7? Maybe 7 is the largest finite number, and 8 is > > > actually infinite? > > Don't be stupid. > He is just trying to come down to your level, TO. Don't DO THAT, and REVERSE IT EACH AND EVERY TIME IT OCCURS. Tony's contradiction was ALREADY CAUGHT when he said that the number of natural numbers is an infinite-indeterminate number. karl m
From: malbrain on 28 Jul 2005 12:56 Virgil wrote: > In article <MPG.1d51ae843adae7ee989fc5(a)newsstand.cit.cornell.edu>, > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > > > > Do you, or do you not, have an infinite set? Do you, or do you not, egenrate > > one member per iteration. How many iterations are requires to produce an > > infinite set, one at a time? (sigh) > > One for each finite natural after the first(sigh). Just because Tony is exhausted after a 40 mile forced march through the Tibetan highlands, is no excuse for you. If you're looking for ways to keep his interest up, try juggling. karl m
From: malbrain on 28 Jul 2005 13:00 Virgil wrote: > In article <MPG.1d51aa051fa66820989fc2(a)newsstand.cit.cornell.edu>, > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > > > > > For example, presumably there is some maximum length > > > to the finite binary strings, which we will call L. > > > How many binary strings are there then? 1 + 2 + 4 + ... + 2^L, > > > which we all know is 2^(L+1)-1, which is finite, and is clearly > > > larger than L (assuming L > 0). Now why someone would believe that > > > there can exists 2^(L+1)-1 binary strings, but there cannot exist > > > binary strings with length 2^(L+1)-1 is quite beyond me. They > > > are both finite numbers. Why is the limit on finite string lengths > > > smaller than the limit on finite sets of finite strings? > > > > It's not > > Then TO has a contradiction on his hands, because as soon as the the > length of a string can equal number of strings, we get a spiralling > increase in both that has no finite limit. Obviously Tony had a contradiction on his hands, or he wouldn't have posted here in the first place. It's a premise, not a conclusion. karl m
From: malbrain on 28 Jul 2005 13:03
Virgil wrote: > In article <MPG.1d51a923cd149b5b989fc1(a)newsstand.cit.cornell.edu>, > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > > > Torkel Franzen said: > > > stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: > > > > > > > >If those lengths cannot be infinite, then the set cannot be either. > > > > > > > > Why do you believe that? > > > > > > As we know, this idea is at the core of innumerable crank postings. > > > Experience strongly suggests that it is impractical to seek > > > elucidation of its roots by direct questioning of the authors of these > > > postings. Conceivably a decisive study could be made of it. No doubt > > > it has manifested itself through the ages, but the net archives > > > provide an unprecedently rich source of data about this peculiar > > > intellectual stumbling block. > > > > > How silly will you feel when you finally come to realize that this unending > > stream of "cranks" were all right, while you maligned, isnulted and bullied > > them? Will you ever apologize, or go to your graves in denial? Gee, I > > wonder.... > > Since this will take a good deal longer to occur that the instanciation > of any of TO's infinite naturals, don't anybody except TO hold your > breath. Children hold their breath in an attempt to provoke fear in their parents. What kind of mixed-methaphor are you peddling? karl m |