An uncountable countable set
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From: Virgil on 20 Sep 2006 23:27 In article <45119a4f(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Mike Kelly wrote: > > > > Even though set theory leads to an arithmetic on natural numbers that > > is identical to everyday arithmetic? > > I have nothing against set theory in general. It's the transfinite > portions which are schlock. They lead to nothing useful, or even sensible. As the transfinite portions are direct consequences of the axioms themselves, TO is saying that he wants to accept only those parts of a unified whole that he can understand, and reject everything he can't. > > > > What does it mean for a conclusion to be incorrect? That it is not a > > logical consequence of one's assumptions? > > It means that it contradicts the greater part of our knowledge in the > area TO has no knowledge of that area. He only has intuition, and his is a good deal less reliable than most. > so there's something wrong, either with the assumptions/data, or > the rules of inference. Or with TO's intuition. The first is a discovery problem, and the second > a matter of mathematics and logic. I would suggest that, while there > area couple of unresolved questions in logic, that the fault with > transfinitology lies in its starting assumptions. Which of the axioms of ZF does TO wish to dump? > > That's not how it works in "the finite realm" in set theory, either. > > Apparently you're completely missing my point, too. > > What? No, you are missing MY point. It's not CONSISTENT with the rest of > mathematics. It's a FICTION. Except that TO cannot point out any point of it which is more fictional than mathematics as a whole. > Not all operations possible with finite numbers are possible with the > T-riffic numbers, but I don't see as they contradict finite numbers in > any way. That TO claims he cannot see a problem is not evidence that no problem exists, as TO's vision in things mathematical has long since been shown to be considerably less than 20/20. Only when TO has produced mathematically valid proofs of his claims will anyone take any of them seriously. Handwaving is not enough TO!
From: Virgil on 20 Sep 2006 23:29 In article <45119add(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Mike Kelly wrote: > > Tony Orlow wrote: > >> Virgil wrote: > >>> In article <450d5f76(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>> > >>> > >>>> Mike, you haven't responded to my use of IFR > >>> An IFR, being dependent on order relations, at best measures order > >>> relations, not their underlying sets. > >> Funny how it DOES measure the sizes of sets perfectly in all finite cases. > > > > So... how do we use IFR to tell us the size of the set {sqrt(17), Pi, > > e, {}, 42 } ? > > > > That's a finite set. You don't need it. Meaning that TO's IFR doesn't even work for finite sets. TO has admitted that cardinality at least works right for finite sets.
From: cbrown on 21 Sep 2006 00:34 Tony Orlow wrote: <snip> > I did give another curve with the same "Tlimit" as the staircase in the > limit, which produced an interesting result, giving weight to the notion > that an infinitesimal is something distinct from 0, whose square is not > distinct from 0. Suppose we let B represent Big'un; then B*1/B = 1, where 1/B is an infinitesimal. Then what you are saying means 1/B = 1/B 1*1/B = 1/B (B*1/B)*1/B = 1/B B*(1/B*1/B) = 1/B B*(1/B^2) = 1/B Since 1/B is infinitesimal, its square is not distinct from 0; so... B*(0) = 1/B 0 = 1/B So 1/B is identical to 0. Where is my error? Cheers - Chas
From: stephen on 21 Sep 2006 00:36 cbrown(a)cbrownsystems.com wrote: > Tony Orlow wrote: > <snip> >> I did give another curve with the same "Tlimit" as the staircase in the >> limit, which produced an interesting result, giving weight to the notion >> that an infinitesimal is something distinct from 0, whose square is not >> distinct from 0. > Suppose we let B represent Big'un; then B*1/B = 1, where 1/B is an > infinitesimal. Then what you are saying means > 1/B = 1/B > 1*1/B = 1/B > (B*1/B)*1/B = 1/B > B*(1/B*1/B) = 1/B > B*(1/B^2) = 1/B > Since 1/B is infinitesimal, its square is not distinct from 0; so... > B*(0) = 1/B > 0 = 1/B > So 1/B is identical to 0. Where is my error? Assuming that Tony's definition of infinitesimal has anything to do with any standard definition of infinitesimal. :) Stephen
From: cbrown on 21 Sep 2006 00:59
Mike Kelly wrote: > imaginatorium(a)despammed.com wrote: <snip> > > Mike Kelly [I think] went all through the stuff about limits > > I've gone over limits with Tony several times. But the "staircase" > example was Chas' (...@cbrownsystems.com). Extremely well done it was > too. A shame Tony wasn't able to appreciate it; I learned quite a lot > myself. > Why, I'm blushing :). Actually, I also learned a lot from the describing - which makes it not a waste that TO apparently garnered nothing from it. Wasn't that Aatu K.'s second reason for arguing with cranks? Cheers - Chas |