Obections to Cantor's Theory (Wikipedia article)
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From: Han de Bruijn on 25 Jul 2005 07:47 Robert Low wrote: > Han de Bruijn wrote: > >> Clearly, it has never crossed their minds that such a nice relationship >> between topology and calculus could possibly esists. > > Apart from trivialities like de Rham cohomology and > the Atiyah-Singer Index theorem, anyway. Allright, I've been fishing. Now give me some fish: references please. Han de Bruijn
From: Robert Low on 25 Jul 2005 08:28 Han de Bruijn wrote: > Robert Low wrote: >> Han de Bruijn wrote: >>> Clearly, it has never crossed their minds that such a nice relationship >>> between topology and calculus could possibly esists. >> Apart from trivialities like de Rham cohomology and >> the Atiyah-Singer Index theorem, anyway. > Allright, I've been fishing. Now give me some fish: references please. http://en.wikipedia.org/wiki/De_Rham_cohomology http://en.wikipedia.org/wiki/Atiyah-Singer_index_theorem and references therein. Or google search and use the references of your own choice.
From: Han de Bruijn on 25 Jul 2005 08:59 Robert Low wrote: > Han de Bruijn wrote: > >> Robert Low wrote: >> >>> Han de Bruijn wrote: >>> >>>> Clearly, it has never crossed their minds that such a nice relationship >>>> between topology and calculus could possibly esists. >>> >>> Apart from trivialities like de Rham cohomology and >>> the Atiyah-Singer Index theorem, anyway. >> >> Allright, I've been fishing. Now give me some fish: references please. > > http://en.wikipedia.org/wiki/De_Rham_cohomology > http://en.wikipedia.org/wiki/Atiyah-Singer_index_theorem > > and references therein. > > Or google search and use the references of your own choice. But, as I suspected, these don't compare with my remarkably _simple_ result. Which nevertheless went unnoticed by mainstream mathematics. Han de Bruijn
From: Dave Seaman on 25 Jul 2005 09:00 On Mon, 25 Jul 2005 10:45:20 +0200, David Kastrup wrote: > There is no room for a bit of error in the tenth place if you are > factoring primes. I can factor primes without looking at any of their places. -- Dave Seaman Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling. <http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>
From: Tony Orlow on 25 Jul 2005 09:15
Sorry, I've been away..... Daryl McCullough said: > Tony Orlow (aeo6) <aeo6(a)cornell.edu> wrote: > > >Essentially, the proof shows that no set can have a larger number > >of naturals in it than the values of all the naturals in it. > > What does "the number of naturals in a set mean"? The "size" of the set, the quantity of elements included in the set, each of which is a unique natural number. > > >If each finite n in N is the size of the set including all m<=n, then each of > >them corresponds to a finite set. > > Right. Each natural number n corresponds to a finite set: the set > of all natural numbers less than n. > > >How do we get an infinite set, then, if m<=n is finite for any finite > >n in N? > > You get an infinite set by (1) Pick some starting number a. > (2) Pick an operation f(x) that, given a number n, returns a new > number that is greater than n. (3) Then form the set > > { a, f(a), f(f(a)), ... } > > That's guaranteed to be infinite. Meaning it goes on forever? If it goes on forever, for an infinite number of iterations, each time incrementing the value of the next element (assuming your f() is successor/increment), then the value of the next element will become infinite. Therefore, if the set contains an infinite number of elements, it will contain elements of infinite value. If it doesn't include any elements of infinite value, then the set cannot be infinite. > > -- > Daryl McCullough > Ithaca, NY > > -- Smiles, Tony |