SCI.MATH POLL - uncountable infinity
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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 23:47 On Jun 3, 7:22 pm, "dannas" <inva...(a)invalid.com> wrote: > >In any case, the OP is NOT an authority on the problem. The problem > >long predates him. > > says you. Says everybody who is entitled to an opinion, which certainly no longer includes you. > He stated his problem clearly, What UTTER bullshit. You yourself have misinterpreted this 3 different ways. You do not do that for things that are clearly stated. > YOU modified it into your problem. Herc is the one WHO DECIDED to talk about OUR problem! The fact that he did so in a way that confused you says a lot more about YOU than it does about us or Herc. This was ALWAYS CANTOR's problem. Herc is NOT contributing anything original here! > > the OP did NOT say natural numbers were written on them, > >Liar. > > you lie again!! shame on you! > > >He said, > >"and the boxes have a unique number written on them." > > which includes all other numbers as he did not specify "Natural" Numbers, by > this he also included Complex numbers. No, I'm sorry, he didn't. That's just an "assumption" that YOU made.
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 23:50 On Jun 4, 2:08 am, Dingo <di...(a)gmail.com> wrote: > All it proves is that you nerds all need to get a life. All THAT proves is that you need to get the hell out of here and into a newsgroup more compatible with YOUR excuse for a life.
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. |