SCI.MATH POLL - uncountable infinity
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From: George Greene on 3 Jun 2010 00:09 On Jun 2, 9:00 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. > > ---------------------------------------------- > > 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. >> It's false. > No explanations or you will spoil the poll, just TRUE or FALSE. Oh, bullshit. An explanation wouldn't "spoil the poll". It would just make your head hurt. The proof is not an existence proof in any case. It's a NON-existence proof. It proves that there IS NO "complete enumeration" (putting all of them, with one in every naturally-numbered box) of the subsets. > Is the 'missing box (set)' central to the powerset proof of uncountable infinity? Of course it is, but being central isn't the same as being the whole story. You can't get from non-existence (of an enumeration) to existence of A NUMBER (for A SIZE) of the collections that are too big to be enumerated. The alternative is that big collections might simply NOT HAVE A SIZE AT ALL. You need some more axioms from set theory to guarantee that the collection of subsets can or will have a size, and even then, it is NOT clear what size THAT is (it is MERELY clear that it is "higher").
From: dannas on 3 Jun 2010 00:34 "|-|ercules" <radgray123(a)yahoo.com> wrote in message news:86od4nFja0U1(a)mid.individual.net... > The powerset proof is exactly this: > > 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 ?" how can I point to a single box, out of an infinity of boxes in an imaginary problem ? you need to reword; Is there a box that contains the numbers of all the boxes that don't contain their own number ?" <snip junk>
From: Virgil on 3 Jun 2010 01:40 In article <hu7dsu$cg4$1(a)news.albasani.net>, "dannas" <invalid(a)invalid.com> wrote: > how can I point to a single box, out of an infinity of boxes in an imaginary > problem ? Use your imaginary hand!
From: George Greene on 3 Jun 2010 01:47 On Jun 3, 12:34 am, "dannas" <inva...(a)invalid.com> wrote: > how can I point to a single box, out of an infinity of boxes in an imaginary > problem ? With its NUMBER, THAT's how. Every box has a natural number on it, as a label. No two boxes have the same number and every natural number is on some box. Actually, you could just dispense with the numbers altogether simply by setting up the boxes in 1 straight line and COUNTING.
From: |-|ercules on 3 Jun 2010 02:29
"George Greene" <greeneg(a)email.unc.edu> wrote ... > On Jun 3, 12:34 am, "dannas" <inva...(a)invalid.com> wrote: >> how can I point to a single box, out of an infinity of boxes in an imaginary >> problem ? > > With its NUMBER, THAT's how. > Every box has a natural number on it, as a label. > No two boxes have the same number and every natural number is on some > box. > Actually, you could just dispense with the numbers altogether simply > by setting > up the boxes in 1 straight line and COUNTING. Thanks George. Care to answer: 1/ is there a box that contains the numbers of all the boxes that don't contain their own number? and 2/ Can the result of 1/ be used to prove the existence of higher infinities? Everyone here is chatting about how smart they are and how my theories are all junk, but no one is answering any of my questions. I'll bet $100 someone replies to the last paragraph while ignoring the 2 questions! Herc |