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Topic: Matheology § 154: Consistency Proof!
Replies: 101   Last Post: Nov 25, 2012 5:08 PM

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 Vurgil Posts: 38 Registered: 1/19/12
Re: Matheology � 154: Consistency Proof!
Posted: Nov 18, 2012 7:04 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> Matheology § 154: Consistency Proof!
>
> The long missed solution of an outstanding problem came from a
> completely unexpected side: Social science proves the consistency of
> matheology by carrying out a poll.
>
> As recently reported (see matheology § 152)
> http://www.hs-augsburg.de/~mueckenh/KB/Matheology.pdf
> mathematics and matheology lead to different values of the continued
> fraction
>
> 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+ = 0 (Cauchy)
> 1/((((((10^0)/10)+10^1)/10)+10^2)/10)+ > 1 (Cantor)

It is not at all clear that these expressions represent any continued
fraction at all.

Finite continued fractions look like
a_0,
or
a_0 + 1/a_1,
or
a_0 + 1/(_ 1 + 1/a_2)
or
a_0 + 1/(a_1 + 1/(a_2 + 1/a_3))
or
a_0 + 1/(a_1 + 1/(a_2 + 1/(a_3 + 1/a_4)))
and so on

where a_0 is necessarily an integer and each of the other a_i's is a
necessarily a POSITIVE integer, with the infinite case merely extending
the finite cases endlessly.

But it is not at all clear what value any of the a_i would have to have
in an expression like
"1/((((((10^0)/10)+10^1)/10)+10^2)/10)+"

Date Subject Author
11/18/12 mueckenh@rz.fh-augsburg.de
11/18/12 Vurgil
11/18/12 William Hughes
11/18/12 Vurgil
11/19/12 mueckenh@rz.fh-augsburg.de
11/19/12 Vurgil
11/19/12 mueckenh@rz.fh-augsburg.de
11/19/12 William Hughes
11/19/12 mueckenh@rz.fh-augsburg.de
11/19/12 Vurgil
11/20/12 mueckenh@rz.fh-augsburg.de
11/20/12 Virgil
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
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11/21/12 William Hughes
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11/22/12 William Hughes
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11/22/12 William Hughes
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11/22/12 William Hughes
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11/22/12 William Hughes
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11/23/12 Virgil
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11/23/12 Virgil
11/23/12 William Hughes
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11/23/12 William Hughes
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11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
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11/23/12 William Hughes
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11/23/12 William Hughes
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11/23/12 William Hughes
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11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
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11/22/12 mueckenh@rz.fh-augsburg.de
11/19/12 Vurgil
11/20/12 mueckenh@rz.fh-augsburg.de
11/20/12 Virgil
11/22/12 David Valdez