Obections to Cantor's Theory (Wikipedia article)
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From: malbrain on 28 Jul 2005 19:42 MoeBlee wrote: > malbr...(a)yahoo.com wrote: > > > MoeBlee wrote: > > > malbrain(a)yahoo.com wrote: > > > > > > > Tied: product of/conclusion from. Let's try Webster: > > > > > > Senses of 'tied to' include 'bound to', 'answerable to', 'obligated to' > > > 'limited by', etc. Other than that, I see no productivity in going > > > further with quibbles about such informal terms. > > > It goes beyond the ties as things-in-themselves into CONNECTIVES, > > FASTENERS and GAUGES. karl m > > You're deep. GAUGES are what rail-ways are all about. In one sense the whole world fought over which one should cross the middle-east. karl m
From: malbrain on 28 Jul 2005 19:50 MoeBlee wrote: > malbr...(a)yahoo.com wrote: > > > MoeBlee wrote: > > > malbrain(a)yahoo.com wrote: > > > > > > You haven't used the term at all, yet. karl m > > > > > > I used the term 'platonist'. > > > > And there's a branch of materialism called VULGAR materialism -- > > refusing to go beyond face value. There's more than meets the eye. > > karl m > > I'll have that laminated for my wallet. Thanks for the tip. So, you're in the services industry? karl m
From: malbrain on 28 Jul 2005 19:52 MoeBlee wrote: > malbr...(a)yahoo.com wrote: > > > MoeBlee wrote: > > > malbrain(a)yahoo.com wrote: > > > > > > You haven't used the term at all, yet. karl m > > > > > > I used the term 'platonist'. > > > > And there's a branch of materialism called VULGAR materialism -- > > refusing to go beyond face value. There's more than meets the eye. > > karl m > > I'll have that laminated for my wallet. Thanks for the tip. So, you're in the services industry? karl m
From: malbrain on 28 Jul 2005 21:29 Virgil wrote: > In article <MPG.1d52e828a17493c1989fdb(a)newsstand.cit.cornell.edu>, > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > > > Daryl McCullough said: > > > Tony Orlow (aeo6) wrote: > > > > > > >Daryl McCullough said: > > > > > > >> So, you agree that for *finite* sets, two sets have the same > > > > > > >> bigulosity if and only if there is a bijection between the two? > > > >> But that no longer holds for infinite sets? > > > >> > > > >> Then how is bigulosity an improvement over cardinality? > > > >Because Bigulosity takes into account the nature of the bijection > > > >in order to determine a precise relative size of infinity. Virgil, this sounds like the same problem as the poster in the other thread -- relative cardinals are not a resolution to cardinal/ordinal contradiction. > > > > > > In other words, bigulosity is whatever you want it to be, and so > > > you have a lot more flexibility. Just make it up as you go along. > > > > > > A = the set of natural numbers { 0, 1, 2, ... } B = the set of > > > base ten numerals { "0", "1", "2", ... } C = the set of base > > > two numerals { "0", "1", "10", "11", "100", ... } > > > > > > A and B have the same bigulosity. A and C have the same bigulosity. > > > But B and C do *not* have the same bigulosity (clearly C has a > > > smaller bigulosity than B). That's bigulosity for you... > > > > > > -- Daryl McCullough Ithaca, NY > > > > > > > > If you consider your numerals to have N digits, then base ten has > > 10^N elements and base 2 has 2^N elements Virgil, we've already used N to represent the set of natural numbers, not its cardinality. I don't think we have agreement that the natural numbers have a mathematical generating function. > So that TO is declaiming that the number of naturals is dependent on the > base in which they are to be represented? That's a WONDERFUL conclusion. We can get somewhere with it. karl m
From: Martin Shobe on 28 Jul 2005 21:45
On Thu, 28 Jul 2005 13:50:09 +0200, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >Martin Shobe wrote: > >> And the gist of our argument is that not being able to "go back to >> earth" is not a problem. Mathematics is not restricted to those >> things that can "go back to earth". >Precisely. But perhaps "_useful_ mathematics" is restricted to those >things that can "go back to earth". No. Some parts of mathematics were designed to bolter other parts of mathematics, and do not need to "go back to earth" (At least not directly). Other parts were designed purely for the gratification of the designers. That is also "useful", and often enough, applications that the original designers never considered are found later. > If we make a distinction between >useful and useless mathematics, formalize it and present that to our >politicians, tax payers and bosses. Would that be a problem? >No? >Just as a matter of prevention, shouldn't we at least _try_ to find >a way of living together, then? Sure thing, let those who wish to concentrate on the mathematics that "go back to earth", work on the mathematics that "go back to earth" and allow them to define their terms as they see fit. Let those who wish to work an mathematics that doesn't, work on mathematics that doesn't, and let them define their terms as they see fit. And when one borrows from the other, remember that those who are being borrowed from do not have to change their theories to suit the borrowers. The borrower is responsible for appropriately applying what was borrowed. Martin |