SCI.MATH POLL - uncountable infinity
in [Physics]
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From: herbzet on 4 Jun 2010 23:38 |-|ercules wrote: > I'll wait and see if someone else takes the bait. > > >> The proof of higher infinities than 1,2,3...oo infinity relies on > >> the fact that there is no box that contains all and only all the > >> label numbers of the boxes that don't contain their own label number. > > TRUE OR FALSE Um, false, so far as I know. We have 1) |N| < |P(N)| 2) |P(N)| <= |R| -------------- .: |N| < |R| but neither of Cantor's proofs that |N| < |R| involves either of premises (1) or (2), as far as I can recall. Perhaps someone will refresh my memory on who first observed that premise (2) is true. -- hz
From: George Greene on 4 Jun 2010 23:42 On Jun 3, 7:22 pm, "dannas" <inva...(a)invalid.com> wrote: > >There IS NO "the" number inside the box! > > He says there is, can't you read? No, he doesn't, and I QUOTED what he said. > > >THE number is ON THE OUTSIDE of the box, as a label, or, as the OP > >said, > >"written on them". > >What is INside each and every box is a ("unique", i.e., different for > >each one) SUBSET > >of the naturals! > > That is not what he said at all, It is so too, dumbass. > he said, "with fridge magnets in the boxes > that are any natural number" Which is EXACTLY WHAT I SAID. Please note that he said magnets PLURAL. Implying natural numbers PLURAL, i.e., A SET of natural numbers. The fact that you didn't figure this out just means you're stupid, not that I have "made assumptions about" what he said. That's what YOU did. BADLY.
From: George Greene on 4 Jun 2010 23:49 On Jun 4, 1:55 am, Transfer Principle <lwal...(a)lausd.net> wrote: > Note that this is _not_ the same as, "do you believe that > _ZFC_ proves that there are more reals than naturals?" For > this isn't open to a vote at all -- there is no debate > that the uncountability of the reals is a theorem of ZFC. Of course there is. Maybe you should google "Lowenheim-Skolem Theorem". ZFC is usually phrased as a FIRST-ORDER theory in standard classical logic WITH FINITE wffs. All such theories have the property that they have COUNTABLE models. If the whole universe is countable then OBVIOUSLY there are NO uncountable parts of it. The relevant theorem of ZFC is that a certain kind of bijection does not occur in the domain (of any model). This winds up having nothing whatsoever to do with uncountability.
From: George Greene on 4 Jun 2010 23:52 On Jun 4, 9:39 am, Marshall <marshall.spi...(a)gmail.com> wrote: > That's not what you said, but fine. So each box has a single natural > number in it? No, dumbass. > That's supposed to be the count of the fridge magnets? No. > And each box has a > unique, possibly different/possibly same natural number written on it? Every box has 1 natural number written on it and some subset of them inside. All the numbers on the outsides are "unique" in the sense that no box has the same number-on-the-outside as any other box; every number occurring on the outside of a box occurs ONCE out there, over the ENTIRE infinity of boxes. There is a lot of deliberate density going on here. Even Herc's lack of writing skill IS NOT a rational excuse for all this mis-parsing.
From: George Greene on 4 Jun 2010 23:55
On Jun 4, 2:37 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > In particular, the > results of a poll which asks "Is CH true?" are > more likely to be accepted No, they are not. Such a poll is incoherent. That question simply cannot have a true Xor false answer. Polling as though it did is flaunting ignorance. What is actually the case is that CH is true in some models of ZFC AND FALSE IN OTHERS. True AND False. AT THE SAME TIME. Though not in the same place. That is just all there is to it. Polls are simply not relevant. There is a fact of the matter. People DO NOT GET TO HAVE opinions. Either they know or they don't. |