On 18/06/2010 5:31 PM, |-|ercules wrote: > "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? > > There is only one type of infinity.
Infinity is a mathematical construct. Before you can even being to discuss it, you have to have a set of axioms. Which set are you using when discussing infinity?
