An uncountable countable set
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From: Han de Bruijn on 18 Sep 2006 07:39 Virgil wrote: > As HdB has not been able to counter any of the mainstream arguments to > the satisfaction of any but himself, they are sufficient. Never underestimate the strength of your opponent. And the influence of 'sci.math' as a free forum. Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 07:41 Virgil wrote: > The impossibility of a uniform distribution over a countable set is a > direct consequence of the relevant definitions. But only for completed infinite sets. > Does HdB wish to argue that there is sensible debate about whether 2 + > 2 need equal 4 in standard decimal notaton? That's a finitary result and hence not relevant for the debate here. Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 07:43 Virgil wrote: > In article <1158492219.125170.245690(a)d34g2000cwd.googlegroups.com>, > Han.deBruijn(a)DTO.TUDelft.NL wrote: > >>About my supposed "ignorance". Read this: >> >>http://hdebruijn.soo.dto.tudelft.nl/QED/singular.pdf >> >>And tell me what the flaws are in the mathematics of this paper. I have >>dozens of the kind. > > One major flaw occurs in the very first paragraph in which you claim > that what is proper for physics governs "the very nature" of what is > true in mathematics. If this is all you can find, then I'm glad to leave it on my account. Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 07:51 Tony Orlow wrote: > Mike Kelly wrote: >> >> *sigh*. Probabilities are *standard* real numbers between 0 and 1. > > *Standard* probabilities are *standard* real numbers from 0 to 1. Yes, but according to mainstream mathematics, infinitesimals are _not_. Hence, in standard mathematics, probabilities cannot be infinitesimals. Shame! (Oh well, is non-standard analysis a part of standard mathematics?) Han de Bruijn
From: Han.deBruijn on 18 Sep 2006 08:57
Mike Kelly wrote: > Cardinality is a convenient way to point out classes of sets that are > bijectible. That's *all* it is so objections of the form "but that's > not what size is for infinite sets" are vacuous. The problem is not so much in "bijectible" but in the fact that the bijectibles are put together in a "proper class". Worse: this class is a thing outside set theory, because a proper class is not a set. How can a thing be so much infinite that it even defeats set theory? Han de Bruijn |