ANTI-CANTOR CLAIM
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From: Sylvia Else on 20 Jun 2010 23:10 On 21/06/2010 1:01 PM, |-|ercules wrote: >> Well that's pretty much what Cantor predicts. The computables are >> countable. The reals aren't, so for any computable, you can find >> uncountably many non-computable reals. You'd expect a lot of diagonals >> not to be in the list either. >> >> Sylvia. > > Oh cripes! That's so funny how you put 1 and 3 together and get 7. > > So FALSE PREMISE doesn't mean not worth discussing now? BWAHAHA > That's a new one, amazing twist of the discussion there, very clever. > > Herc I thought we were permuting a list of countable reals. Perhaps not. Anyway, go back to the central point. Why do we need to consider permutations at all? Sylvia.
From: |-|ercules on 21 Jun 2010 02:35 "Sylvia Else" <sylvia(a)not.here.invalid> wrote... > On 21/06/2010 1:01 PM, |-|ercules wrote: >>> Well that's pretty much what Cantor predicts. The computables are >>> countable. The reals aren't, so for any computable, you can find >>> uncountably many non-computable reals. You'd expect a lot of diagonals >>> not to be in the list either. >>> >>> Sylvia. >> >> Oh cripes! That's so funny how you put 1 and 3 together and get 7. >> >> So FALSE PREMISE doesn't mean not worth discussing now? BWAHAHA >> That's a new one, amazing twist of the discussion there, very clever. >> >> Herc > > I thought we were permuting a list of countable reals. Perhaps not. > > Anyway, go back to the central point. Why do we need to consider > permutations at all? > > Sylvia. Because the diagonal is a list construct, computable reals is a set. Herc
From: Sylvia Else on 21 Jun 2010 03:22 On 21/06/2010 4:35 PM, |-|ercules wrote: > "Sylvia Else" <sylvia(a)not.here.invalid> wrote... >> On 21/06/2010 1:01 PM, |-|ercules wrote: >>>> Well that's pretty much what Cantor predicts. The computables are >>>> countable. The reals aren't, so for any computable, you can find >>>> uncountably many non-computable reals. You'd expect a lot of diagonals >>>> not to be in the list either. >>>> >>>> Sylvia. >>> >>> Oh cripes! That's so funny how you put 1 and 3 together and get 7. >>> >>> So FALSE PREMISE doesn't mean not worth discussing now? BWAHAHA >>> That's a new one, amazing twist of the discussion there, very clever. >>> >>> Herc >> >> I thought we were permuting a list of countable reals. Perhaps not. >> >> Anyway, go back to the central point. Why do we need to consider >> permutations at all? >> >> Sylvia. > > Because the diagonal is a list construct, computable reals is a set. > That's really not an answer. Sylvia.
From: Barb Knox on 23 Jun 2010 22:08 In article <a6472a72-772c-448f-a443-651d575b41bf(a)k39g2000yqd.googlegroups.com>, TCL <tlim1(a)cox.net> wrote: > On Jun 20, 8:56�pm, George Greene <gree...(a)email.unc.edu> wrote: > > On Jun 20, 3:33�pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: [SNIP] > Now I understand why it was so hard for me to make some of my worst > students to understand mathematics. "Herc" is not a useful model of your non-understanding students, unless you were teaching at a mental institution. Seriously -- he is a diagnosed schizophrenic who at one time was locked up. Of course, one does all-too-frequently encounter similar invincible ignorance among students who don't have that particular excuse. -- --------------------------- | BBB b \ Barbara at LivingHistory stop co stop uk | B B aa rrr b | | BBB a a r bbb | Quidquid latine dictum sit, | B B a a r b b | altum videtur. | BBB aa a r bbb | -----------------------------
From: George Greene on 24 Jun 2010 02:14
On Jun 20, 10:08 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > > > On 21/06/2010 5:33 AM, |-|ercules wrote: > >> The antidiagonal is too general to meaningfully define a number. That is a false premise. > > >> It's not just based on all digits in > >> forall n, L(n,n) Yes, actually, it is. > > >> The antidiagonal argument also has to work on EVERY PERMUTATION of a list. It works ON ALL lists. But it only works on THE DIAGONAL of each list. Precisely as you just said IT WASN'T, IT IS based on "all digits in forall n, L(n,n)" whateverthefuck THAT means (nobody who could actually do math would say it that way). > "Sylvia Else" <syl...(a)not.here.invalid> wrote > > It does work. You often get different numbers as a result, but all the > You just said it was a FALSE PREMISE. She did NOT say that THAT was a false premise! She said that YOUR "It's too general to meaningfully define a number" was a false premise. THAT IS a false premise. The definition of the anti- diagonal IS NOT very general: it's very SPECIFIC. IT IS "just based on all digits in forall n, L(n,n)". The point is, that's not THE ONLY way to do it. ANY COMPUTABLE way of selecting a DIFFERENT column from every row WOULD SUFFICE (as will all the myriad UNcomputable ways, except those would have the property that because we couldn't compute them, you would swear that we couldn't actually be doing it, or that they couldn't actually exist). |