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Topic: § 424 Actual Infinity: We never get it - but
we get it!

Replies: 17   Last Post: Feb 10, 2014 4:24 AM

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wolfgang.mueckenheim@hs-augsburg.de

Posts: 644
Registered: 10/18/08
Re: § 424 Actual Infinity: WM never got it - but we
get it!

Posted: Feb 10, 2014 3:31 AM
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Am Montag, 10. Februar 2014 00:15:19 UTC+1 schrieb Virgil:
> In article <a60f8f4f-d749-481a-a8b6-b8d01334a560@googlegroups.com>,
>
> WM <wolfgang.mueckenheim@hs-augsburg.de> wrote:
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>
>

> > Am Sonntag, 9. Februar 2014 21:50:37 UTC+1 schrieb Virgil:
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> >
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> >
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> > > > Note that if there were any solitary antidiagonal, there would have to be
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> > > > first d_n completing it
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>
>

> > > How can there be a digit completing what has no last digit?
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>
>

> > It cannot be. That's why an infinite string of digits does not determine a
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> > real number.
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> That has nothing to do with whether an infinite string of digits can
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> determine real number.


It has. Compare § 430 of today.
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>
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> Given a radix position in that string and a base, every different such
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> infinite string corresponds to a different real number.


Not at all. A string of digits does not definbe a number. It is possible to define real numbers that have the asserted strings. But that requires finite definitions.
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>
>
> If WM thinks otherwise, let him present such a string, with specified
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> base and radix point, that he claims does NOT represent a real number.


The string 0.59765 does not represent a real number unless you define that only zeros (or any other definable sequence of digits) will follow. That, however, requires a finite definition.
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>
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> > > > And note that the definition of a number has to have an end-signal.
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>
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> But any infinite sequence's "end signal" indicates infinitely many terms
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> before it takes effect.


Therefore the digits that will follow have to be defined by a finite expression.
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> > >
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> > >
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> > >
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> > > The defnition of an infinite sequence doe not require it to have a last
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> > > term.
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> >
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> > The definition _of_ the sequence is finite. That determines a limit. The
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> > definition _by_ the terms of the sequnece does not exist.
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>
>
> But definition by the terms of the sequENce dose.
>


No.


Regards, WM



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