Give me ONE digit position of any real that isn't computable up to that digit position!
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From: Marshall on 10 Jun 2010 20:03 On Jun 10, 1:25 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > All I want is for everyone > to have the opportunity to _choose_ a set theory > that best reflects his own intuition. I want a pony. Marshall
From: FredJeffries on 10 Jun 2010 23:27 On Jun 10, 3:33 pm, herbzet <herb...(a)gmail.com> wrote: > Transfer Principle wrote: > > According to Holmes, Cantor's proof does show that > > P1(A), the set of singleton subsets of A, does have > > a smaller cardinality than P(A). But P1(A) often > > doesn't have the same size as A, > > That is, it is smaller. In those cases, what, I > wonder, are the elements x of A that don't have > unit sets {x}? I haven't had time to study this, but I would guess that if V is the set of all sets then there is no unit set {V} ?
From: George Greene on 11 Jun 2010 17:56 On Jun 4, 5:55 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > A computer can calculate ANY digit sequence up to INFINITE length. No, it can't. > Sci.math will make a minor correction there, a computer can only calculate > all digit sequences up to ALL finite lengths. Sci.logic will make this correction too. The fact that you think it is "minor" means you should give up and go home. > This is like saying a computer can only calculate all digit sequences up to INFINITE finite lengths. No, it ISN'T like that. It isn't like that because "this" actually makes sense and is grammatical in English, whereas yours, "INFINITE finite lengths", is completely nonsensical. There is no such thing as an "INFINITE finite" anything, lengths or otherwise. INFINITE and "finite" ARE CONTRADICTORY or mutually exclusive. Everybody who can actually speak English knows that.
From: herbzet on 11 Jun 2010 23:04 FredJeffries wrote: > herbzet wrote: > > Transfer Principle wrote: > > > > According to Holmes, Cantor's proof does show that > > > P1(A), the set of singleton subsets of A, does have > > > a smaller cardinality than P(A). But P1(A) often > > > doesn't have the same size as A, > > > > That is, it is smaller. In those cases, what, I > > wonder, are the elements x of A that don't have > > unit sets {x}? > > I haven't had time to study this, but I would guess that if V is the > set of all sets then there is no unit set {V} ? I don't know, Fred, I don't know much about NF either, but that seems like a good guess. I think that the set universe V in NF is symmetrical between "large" and "small" sets -- that is, the complement of any set A exists, V - A. This is different from ZFC in that the complement of a set in ZFC doesn't exist -- or at least, it can't be proved to exist, I'm unclear on that point. It is usually said that the complement is "too large" to be a set. My guess is that the sets in NF that aren't equinumerous with the set of their respective singleton subsets are all among the "large" sets, but that's just a wild guess on my part. While we're here, I might as well mention that talking about ZF(C) set theory and other set theories is a more-or-less permanent fixture of the scene here in sci.logic, but I must confess I've never been clear about why that is. If one is especially interested in a consistent foundation for mathematics, then I guess that would explain all the interest, but it's never been made clear to me why it would be of particular interest to the study of logic in general. Consequently, I've never put much effort into mastering all the nit-picking details of any set theory. I get the impression that perhaps set theory is roughly equivalent to the study of higher-order logics. Maybe that's the reason people talk about it so much here. -- hz
From: MoeBlee on 12 Jun 2010 14:17
On Jun 12, 11:11 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > MoeBlee wrote: > > On Jun 9, 6:50 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > >> Nam > >> Nguyen > > > is overwhelmingly confused about some of the most basic matters in > > mathematical logic, and worse, (with rare exception) he will not allow > > himself to be corrected, educated, or enlightened by the many quite > > informed posters who try. It is usually a dead end trying to have a > > rational discussion with Nguyen. This is shown over and over again in > > thread after thread. And it's definitely not a matter of "a new > > theory" but rather that he purports to represent a correct > > understanding of standard, ordinary mathematical logic while yet he's > > horribly mixed up about it. > > The voice of a _pathetic_ incarnation of the Inquisition. > I had some technical issues to discuss about a new ZF axiom, > about FOL based definition of AI and Moeblee has nothing to > respond or to post except very pathetic trashing! A poster asserted his appraisal of you. I have a different appraisal and asserted it. I can't possibly predict every "technical issue you have to discuss about a new ZF axiom and FOL based definition of AI". And I'm not stopping you from discussing it. MoeBlee |