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
