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

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ross.finlayson@gmail.com

Posts: 2,713
Registered: 2/15/09
Re: Another AC anomaly?
Posted: Dec 27, 2009 3:23 PM
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On Dec 22, 5:38 pm, Marshall <marshall.spi...@gmail.com> wrote:
> On Dec 22, 5:27 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>
> wrote:
>

> > On Dec 19, 5:20 pm, Virgil <Vir...@home.esc> wrote:
>
> > > Not at all!
>
> > > I merely note that every rational integer is included among the reals,
> > > in both the Dedekind construction and the Cauchy construction, and 1 is
> > > nicely both rational and integral.

>
> > Oh, so 1 = 1.000... now, eh.
>
> > Good luck with that.
>
> He won't need it. 1 the ratio is the same number as 1
> the natural, is the same number as 1 the member of
> any other set.
>
> Unless you confuse numbers and their representations.
>
> Marshall


In set theory there are only sets.

Of course I think that 1 = 1.000..., but it makes a Platonist out of
you.

Consider the general construction via ordinals of the naturals, vis-a-
vis a standard construction of the reals. If you want to encode their
representations then it's of products of sets, for example those.

So, implicitly, writing "1 = 1.000..." encodes both of them. There
are simpler ways to model various real-valued processes.

There are more obvious consequences, more of them. Area is the sum.

Rationals have much simpler encodings than the general standard case,
which finds itself "incomplete" in being the "complete" ordered field,
in that each arithmetic operation would be definite, constructively
then via completeness, Dedekind/Cauchy/Eudoxus constructions are
insufficient to model the real, real numbers, number-theoretically.

Rationals are dense in the reals.

Ross


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

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