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

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 154: Consistency Proof!
Posted: Nov 21, 2012 10:10 AM

On 21 Nov., 14:10, William Hughes <wpihug...@gmail.com> wrote:
> It is not enough to
> give a an infinite process and declare a limit.

But it is enough to to consider the following sequence
> >> > 01.
> >> > 0.1
> >> > 010.1
> >> > 01.01
> >> > 0101.01
> >> > 010.101
> >> > 01010.101
> >> > 0101.0101
> >> > ...

to see that it has the (improper) limit
(((?((((((10^0)/10)+10^1)/10)+10^2)/10)+? )+10^n)/10)+?
infinite.
.
And it is as easy to see that in set theory the set of indices left of
the decimal point
> >> > 0_2 1_1 .
> >> > 0_2 . 1_1
> >> > 0_4 1_3 0_2 . 1_1
> >> > 0_4 1_3 . 0_2 1_1
> >> > 0_6 1_5 0_4 1_3 . 0_2 1_1
> >> > 0_6 1_5 0_4 . 1_3 0_2 1_1
> >> > 0_8 1_7 0_6 1_5 0_4 . 1_3 0_2 1_1
> >> > 0_8 1_7 0_6 1_5 . 0_4 1_3 0_2 1_1
> >> > ...

has limit { }.

And it is further easy to know, that decimal fractions as conceived by
Simon Stevinus cannot contain numerals without indices, even if no one
does see them because they were not explicitly written.

Regards, WM

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
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
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
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
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
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12
11/23/12 Virgil
11/24/12 mueckenh@rz.fh-augsburg.de
11/24/12 Virgil
11/23/12 Virgil
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11/24/12 Virgil
11/25/12 mueckenh@rz.fh-augsburg.de
11/25/12 Virgil
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11/25/12 Virgil
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 Virgil
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 Virgil
11/23/12 Virgil
11/23/12 Virgil
11/22/12 Virgil
11/22/12 Virgil
11/22/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/22/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/22/12 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