"Sylvia Else" <sylvia@not.here.invalid> wrote ... > On 19/06/2010 12:45 PM, |-|ercules wrote: >> "Sylvia Else" <sylvia@not.here.invalid> wrote >>> On 19/06/2010 6:50 AM, WM wrote: >>>> On 18 Jun., 09:37, Sylvia Else<syl...@not.here.invalid> wrote: >>>>> On 18/06/2010 5:31 PM, |-|ercules wrote: >>>>> >>>>> >>>>> >>>>> >>>>> >>>>>> "Sylvia Else"<syl...@not.here.invalid> wrote ... >>>>>>> On 18/06/2010 4:52 PM, |-|ercules wrote: >>>>>>>> "Sylvia Else"<syl...@not.here.invalid> wrote ... >>>>>>>>> On 18/06/2010 3:03 PM, |-|ercules wrote: >>>>>>>>>> "Sylvia Else"<syl...@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. >>>> >>>> What was the set that Cantor used? >>>> Nevertheless he "proved". >>> >>> He certainly was using some. For example, the diagonal argument falls >>> apart if the axioms don't permit the construction of a number by >>> choosing digits different from those on the diagonal. >>> >>> It isn't even clear whether Herc is tying to invalidate Cantor's proof >>> by finding a mistake in it, or to prove the inverse, which wouldn't >>> invalidate Cantor's proof, but would only show that the axioms on >>> which it is based are inconsistent. >>> >>> Herc cannot avoid the need to specify the set of axioms. >>> >>> Sylvia. >> >> How would one dispute axiomatic deductions if that were the case? > > What do you mean by "axiomatic deduction"? >> >> Are you saying all mathematical facts are either axioms or the result of >> (X & X->Y) -> Y >> ? > > Mathematics consists of axioms and statements (theorems) that can be > proved from those axioms. The axioms cannot themselves be proved, nor > disproved, though they may be shown to be inconsistent with one another. > > Sometimes the axioms seem so self-evidently true that people aren't even > aware that they're there. But they are, if you look. > > Sylvia.
blah blah blah...
you skipped my question, but don't bother I wasn't arguing anything just seeing if you knew what you were talking about.
