SCI.MATH POLL - uncountable infinity
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From: Marshall on 4 Jun 2010 09:04 On Jun 3, 10:55 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > Here's how I think this poll should be asked: > > "Do you believe that there are more reals than naturals?" Yes. > Those for whom ZFC is the > preferred theory are likely to question the legitimacy of > any poll in which a majority believe in any statement > refuted by ZFC. This is a profoundly stupid statement. Marshall
From: Marshall on 4 Jun 2010 09:06 On Jun 3, 11:09 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > > For a (infinite) list of uniquely numbered boxes containing (possibly infinite amount of) fridge magnet numbers > > 1/ Is there a box that contains the numbers of all the boxes that don't contain their own number? I thought you said the boxes contain fridge magnets. I honestly don't understand this question. Marshall
From: |-|ercules on 4 Jun 2010 09:22 "Marshall" <marshall.spight(a)gmail.com> wrote > On Jun 3, 11:09 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: >> >> For a (infinite) list of uniquely numbered boxes containing (possibly infinite amount of) fridge magnet numbers >> >> 1/ Is there a box that contains the numbers of all the boxes that don't contain their own number? > > I thought you said the boxes contain fridge magnets. I honestly don't > understand this question. > > > Marshall You're joking aren't you? There's BOXES with NUMBERS in them. What can you possibly be missing fool? Herc
From: Marshall on 4 Jun 2010 09:39 On Jun 4, 6:22 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "Marshall" <marshall.spi...(a)gmail.com> wrote > > > On Jun 3, 11:09 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > > >> For a (infinite) list of uniquely numbered boxes containing (possibly infinite amount of) fridge magnet numbers > > >> 1/ Is there a box that contains the numbers of all the boxes that don't contain their own number? > > > I thought you said the boxes contain fridge magnets. I honestly don't > > understand this question. > > > Marshall > > You're joking aren't you? There's BOXES with NUMBERS in them. That's not what you said, but fine. So each box has a single natural number in it? That's supposed to be the count of the fridge magnets? And each box has a unique, possibly different/possibly same natural number written on it? Is that the setup? > What can you possibly be missing fool? A clear description. I think Transfer Principle's question was a lot easier to understand. Marshall
From: MoeBlee on 4 Jun 2010 12:06
On Jun 2, 8:00 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > Assume a large/infinite room full of boxes with fridge magnets in the boxes that are any natural number, and the boxes have a unique > number written on them. > > "Which box contains the numbers of all the boxes that don't contain their own number ?" > > is proven (by Cantor) to be nonexistent. That's garbled. Cantor didn't prove a QUESTION to be nonexistent. Also, you've left out the crucial "and only" clause. Maybe what you mean is this: Suppose there is a room with boxes in it, such that each box in the room has one or more (or, could be zero or more, too) numbers in it, and each box in the room has a label number. Is there a box in the room that has in it all and only the label numbers of boxes that do not have in them their own label number? There is no such box, since if there is such a box, then the label number of the box is in the box if and only if the label number of the box is not in the box. > Is the following statement TRUE or FALSE? > > << The fact that there is no box that contains the numbers of all the boxes >> > << that don't contain their own number proves that higher infinities exist. >> That assumes a fact that you've miststated. A correct statement is: There is no box that contains the label numbers of all AND ONLY those boxes that don't contain their own label number. Also, the word 'prove' is ambiguous. In formal mathematics, we prove sentences relative to formal systems, while also 'prove' means to provide convincing basis for belief (or something to that effect). Your example about the boxes is an analogy of a proof in certain formal systems that no set is equinumerous with its power set, and also an analogy with an argument, aside from any formal system, that many mathematicians take as convincing toward the conclusion that no set is equinumerous with its power set, and such proofs, along with other principles, lead to a proof that there exist sets that are uncountable. What's your point in asking the question? MoeBlee |