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

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 154: Consistency Proof!
Posted: Nov 21, 2012 4:01 PM

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

> 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 { }.

While I see a point between other expressions , I do not see anything
that could be properly interpreted as a DECIMAL point.

Or does WM regard such things as 1_3 and 1_5 as decimal digits?

Furthermore in standard mathematics

02 11 . has 2 "indices left of the point"
...
08 17 06 15 . 04 13 02 11 has 4 "indices left of the point"

And the limit of number of "positions" would be infinite on either side
of that point.

On the other hand, the limit of the set on the left minus the set on the
right would be empty.

Though
--

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
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11/19/12 William Hughes
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11/19/12 Vurgil
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11/20/12 Virgil
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11/21/12 William Hughes
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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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11/21/12 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
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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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11/22/12 David Valdez