"Sylvia Else" <sylvia@not.here.invalid> wrote ... > On 18/06/2010 4:52 PM, |-|ercules wrote: >> "Sylvia Else" <sylvia@not.here.invalid> wrote ... >>> On 18/06/2010 3:03 PM, |-|ercules wrote: >>>> "Sylvia Else" <sylvia@not.here.invalid> wrote >>>>> On 18/06/2010 10:40 AM, Transfer Principle wrote: >>>>>> On Jun 17, 6:56 am, Sylvia Else<syl...@not.here.invalid> wrote: >>>>>>> On 15/06/2010 2:13 PM, |-|ercules wrote: >>>>>>>> the list of computable reals contain every digit of ALL possible >>>>>>>> infinite sequences (3) >>>>>>> Obviously not - the diagonal argument shows that it doesn't. >>>>>> >>>>>> But Herc doesn't accept the diagonal argument. Just because >>>>>> Else accepts the diagonal argument, it doesn't mean that >>>>>> Herc is required to accept it. >>>>>> >>>>>> Sure, Cantor's Theorem is a theorem of ZFC. But Herc said >>>>>> nothing about working in ZFC. To Herc, ZFC is a "religion" >>>>>> in which he doesn't believe. >>>>> >>>>> Well, if he's not working in ZFC, then he cannot make statements about >>>>> ZFC, and he should state the axioms of his system. >>>> >>>> Can you prove from axioms that is what I should do? >>>> >>>> If you want to lodge a complaint with The Eiffel Tower that the lift is >>>> broken >>>> do you build your own skyscraper next to the Eiffel Tower to demonstrate >>>> that fact? >>>> >>> >>> That's hardly a valid analogy. >>> >>> If you're attempting to show that ZFC is inconsistent, then say that >>> you are working within ZFC. >>> >>> If you're not working withint ZFC, then you're attempting to show that >>> some other set of axioms is inconsistent, which they may be, but the >>> result is uninteresting, and says nothing about ZFC. >>> >>> Sylvia. >> >> >> That would be like finding a fault with the plans of The Leaning Tower >> Of Piza. >> >> I might look at ZFC at some point, but while you're presenting Cantor's >> proof >> in elementary logic I'll attack that logic. >> >> Instead of 'constructing' a particular anti-diagonal, your proof should >> work equally >> well by giving the *form* of the anti-diagonal. >> >> This is what a general diagonal argument looks like. >> >> For any list of reals L. >> >> CONSTRUCT a real such that >> An AD(n) =/= L(n,n) >> >> Now to demonstrate this real is not on L, it is obvious that >> An AD(n) =/= L(n,n) >> >> Therefore >> [ An AD(n) =/= L(n,n) -> An AD(n) =/= L(n,n) ] proves superinfinity! >> >> And THAT is Cantor's proof! >> >> Want to see his other proof? That no box contains the box numbers (of >> boxes) that >> don't contain their own box number? >> That ALSO proves superinfinity! >> >> Great holy grail of mathematics you have there. >> >> Herc > > What are you trying to prove?
