Why can no one in sci.math understand my simple point?
in [Logic]
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From: Tim Little on 18 Jun 2010 02:58 On 2010-06-18, Peter Webb <webbfamily(a)DIESPAMDIEoptusnet.com.au> wrote: > Because Cantor's proof requires an explicit listing. This is a very > central concept. Cantor's proof works on any list, explicit or not. The rest of your misconception snipped. - Tim
From: Sylvia Else on 18 Jun 2010 03:14 On 18/06/2010 4:52 PM, |-|ercules wrote: > "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... >> On 18/06/2010 3:03 PM, |-|ercules wrote: >>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>>> On 18/06/2010 10:40 AM, Transfer Principle wrote: >>>>> On Jun 17, 6:56 am, Sylvia Else<syl...(a)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? Sylvia.
From: |-|ercules on 18 Jun 2010 03:31 "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... > On 18/06/2010 4:52 PM, |-|ercules wrote: >> "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... >>> On 18/06/2010 3:03 PM, |-|ercules wrote: >>>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>>>> On 18/06/2010 10:40 AM, Transfer Principle wrote: >>>>>> On Jun 17, 6:56 am, Sylvia Else<syl...(a)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. -oo <--|---|---|---0---|---|---|--> oo Where's yours go? Herc
From: Sylvia Else on 18 Jun 2010 03:37 On 18/06/2010 5:31 PM, |-|ercules wrote: > "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... >> On 18/06/2010 4:52 PM, |-|ercules wrote: >>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote ... >>>> On 18/06/2010 3:03 PM, |-|ercules wrote: >>>>> "Sylvia Else" <sylvia(a)not.here.invalid> wrote >>>>>> On 18/06/2010 10:40 AM, Transfer Principle wrote: >>>>>>> On Jun 17, 6:56 am, Sylvia Else<syl...(a)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? Sylvia.
From: Ostap Bender on 18 Jun 2010 03:42
Because you are too brilliant for the rest of Humankind. |