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Topic: Another AC anomaly?
Replies: 280   Last Post: Dec 27, 2009 3:53 PM

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mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05
Re: Another AC anomaly?
Posted: Dec 11, 2009 10:15 AM
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On 11 Dez., 03:40, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
> In article <5333fb9a-1670-4fcc-85d3-25e75fb5b...@f16g2000yqm.googlegroups.com> WM <mueck...@rz.fh-augsburg.de> writes:
>  > On 10 Dez., 16:29, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
>  >
>  > > Without the axiom of infinity omega would not be immediately existing.
>  > > So apparently there is a definition of omega without the axiom of
>  > > infinity.
>  > > Can you state that definition?
>  >
>  > Look into Cantor's papers. Look into my book.
>
> I have never seen there a proper definition of omega.
>

I knew you did not read it.

Look at p. 93. There the natural numbers are constructed.
On p. 86 all ordinals till eps^eps^eps^... are given. On p. 90 you see
the axiom of infinity 7.

>  > > There are no concepts of mathematics without definitions.
>  >
>  > So? What is a set?
>
> Something that satisfies the axioms of ZF for instance.


Is that a definition?

But in case you shouldn't have been able to find a definition of
actual infinity, here is more than that: omega + 1.

>  > If an infinite set exists as a limit, then it has gotten from the
>  > finite to the infinite one by one element. During this process there
>  > is no chance for any divergence between this set-function and its
>  > cardinality.
>
> If a function exists as a limit, then it has gotten from the finite to
> the infinite one by one step.  During this process there is no chance
> of any divergence between the function and the integral.
>
> Now, what is wrong with that reasoning?
>
> Stronger:
>    lim(n -> oo) 1/n = 0
>    1/n > 0


I do not understand. Do you see a gap here?
>
> If a number exists as a limit, then it has gotten from the finite to the
> infinite one by one step.  During this process there is no chance of any
> divergence between the element and the inequality.
>
> What is wrong with that reasoning?
>
> You are assuming that taking a limit is a final step in a sequence of steps.
> In the definition I gave for the limit of a sequence of sets there is no
> final step.


I did not say that there is a final step. I say that there is no
chance for a difference of lim card(S_n) and card(lim(S_n)) where lim
means n --> oo.

If, in your example you would claim that lim(1/n) = 0 and and 1/omega
= 10, I would not accept such behaviour as mathematics (like your
funny Sum n = 0 or Euler's -1/12).

Regards, WM



Date Subject Author
11/23/09
Read Re: Another AC anomaly?
Jesse F. Hughes
11/23/09
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Herman Jurjus
11/23/09
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master1729
11/25/09
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T.H. Ray
11/24/09
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george
12/1/09
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george
11/25/09
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11/26/09
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Daryl McCullough
11/30/09
Read What's wrong with supertasks? (was Re: Another AC anomaly?)
Herman Jurjus
12/1/09
Read Jesse Hughes of Bentley College uses signature block to defame
others; Ann Reeves Re: What's wrong with supertasks?
plutonium.archimedes@gmail.com
12/1/09
Read Re: Jesse Hughes of Bentley College uses signature block to defame
others; Ann Reeves Re: What's wrong with supertasks?
Marshall
12/1/09
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Bentley College
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12/1/09
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others; Ann Reeves Re: What's wrong with supertasks?
Seth Breidbart
12/1/09
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of Bentley College
Marshall
12/2/09
Read Re: using signature-blocks to defame innocent people Re: Jesse Hughes
of Bentley College
Marshall
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/26/09
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mueckenh@rz.fh-augsburg.de
11/28/09
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mueckenh@rz.fh-augsburg.de
11/28/09
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Virgil
11/26/09
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William Hughes
11/28/09
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William Hughes
11/26/09
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mueckenh@rz.fh-augsburg.de
11/28/09
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ross.finlayson@gmail.com
11/28/09
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Virgil
11/29/09
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mueckenh@rz.fh-augsburg.de
11/29/09
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Virgil
11/29/09
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ross.finlayson@gmail.com
11/29/09
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Marshall
11/30/09
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Virgil
11/30/09
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ross.finlayson@gmail.com
11/30/09
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ross.finlayson@gmail.com
11/30/09
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Virgil
11/30/09
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ross.finlayson@gmail.com
11/30/09
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Virgil
11/30/09
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ross.finlayson@gmail.com
11/30/09
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Virgil
11/29/09
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mueckenh@rz.fh-augsburg.de
11/26/09
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LauLuna
11/26/09
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William Hughes
11/26/09
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anonymous.rubbertube@yahoo.com
11/29/09
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William Hughes
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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11/27/09
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11/29/09
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11/30/09
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mueckenh@rz.fh-augsburg.de
11/30/09
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Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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Virgil
11/27/09
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William Hughes
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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11/27/09
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Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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Dik T. Winter
11/27/09
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mueckenh@rz.fh-augsburg.de
11/30/09
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Dik T. Winter
11/30/09
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mueckenh@rz.fh-augsburg.de
11/30/09
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Virgil
12/1/09
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Dik T. Winter
12/1/09
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mueckenh@rz.fh-augsburg.de
12/1/09
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Dik T. Winter
12/1/09
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mueckenh@rz.fh-augsburg.de
12/1/09
Read Re: Another AC anomaly?
William Hughes
12/1/09
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Virgil
12/1/09
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mueckenh@rz.fh-augsburg.de
12/1/09
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Virgil
12/1/09
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ross.finlayson@gmail.com
12/1/09
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Virgil
12/1/09
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ross.finlayson@gmail.com
12/1/09
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12/2/09
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12/2/09
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mueckenh@rz.fh-augsburg.de
12/2/09
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12/2/09
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12/3/09
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12/3/09
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12/3/09
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12/7/09
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12/8/09
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12/9/09
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12/9/09
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12/9/09
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12/10/09
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12/9/09
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12/9/09
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12/10/09
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12/10/09
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12/10/09
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12/10/09
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12/11/09
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12/15/09
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12/15/09
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12/15/09
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12/17/09
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12/18/09
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12/18/09
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12/18/09
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12/19/09
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12/19/09
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12/22/09
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12/22/09
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12/18/09
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12/19/09
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12/19/09
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12/21/09
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12/21/09
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12/21/09
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12/21/09
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12/22/09
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12/27/09
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12/27/09
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12/16/09
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mueckenh@rz.fh-augsburg.de
12/16/09
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12/11/09
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12/11/09
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12/11/09
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12/11/09
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12/12/09
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12/12/09
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12/12/09
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12/11/09
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12/10/09
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12/10/09
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12/10/09
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12/10/09
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12/10/09
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12/11/09
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12/7/09
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12/8/09
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12/8/09
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12/8/09
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12/8/09
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12/8/09
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12/8/09
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12/10/09
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12/3/09
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12/3/09
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12/3/09
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12/7/09
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12/7/09
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12/7/09
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12/7/09
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12/8/09
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12/8/09
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12/8/09
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12/10/09
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12/10/09
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mueckenh@rz.fh-augsburg.de
12/10/09
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12/10/09
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12/11/09
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12/11/09
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12/11/09
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12/15/09
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12/16/09
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mueckenh@rz.fh-augsburg.de
12/16/09
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12/16/09
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mueckenh@rz.fh-augsburg.de
12/17/09
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T.H. Ray
12/17/09
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Dik T. Winter
12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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Virgil
12/4/09
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Marshall
12/7/09
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Dik T. Winter
12/7/09
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mueckenh@rz.fh-augsburg.de
12/7/09
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Virgil
12/8/09
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Dik T. Winter
12/8/09
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mueckenh@rz.fh-augsburg.de
12/8/09
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12/10/09
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12/10/09
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mueckenh@rz.fh-augsburg.de
12/10/09
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12/10/09
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Dik T. Winter
12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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12/11/09
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12/12/09
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12/12/09
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12/12/09
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12/12/09
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12/12/09
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12/18/09
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12/19/09
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12/19/09
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12/19/09
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12/19/09
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12/19/09
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Virgil
12/19/09
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12/27/09
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12/27/09
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12/27/09
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12/27/09
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12/27/09
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12/27/09
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12/13/09
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12/4/09
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12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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12/4/09
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12/4/09
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12/5/09
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12/5/09
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12/5/09
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12/6/09
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12/5/09
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12/2/09
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12/1/09
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12/1/09
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11/27/09
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11/27/09
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11/30/09
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William Hughes
11/27/09
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11/27/09
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11/27/09
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11/27/09
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11/27/09
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11/27/09
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11/27/09
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11/27/09
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11/27/09
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Virgil
11/27/09
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11/27/09
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William Hughes
11/27/09
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11/27/09
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Virgil

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