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Re: Matheology § 162
Posted:
Nov 26, 2012 1:49 AM
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On 25 Nov., 23:49, Nam Nguyen <namducngu...@shaw.ca> wrote:
> On 25/11/2012 3:11 PM, Roland Franzius wrote:
>
> > Am 25.11.2012 22:37, schrieb WM:
> >> If any of these aspects is computed by another than the analytical
> >> method and turns out as deviating from the analytical result, then the
> >> other method is not suitable for analytical purposes.
>
> > The same statement seems to be true for the problem of different ways of
> > reasoning with different results.
>
> > Most people do not accept wrong methods with wrong results.
> > Wrong methods leading to correct results are widely used everywhere
> > except in mathematics.
>
> There are cases of wrong methods leading to a result that can't be
> determined to be correct or incorrect, in mathematics.
>
In analysis there are cases that can be determined to be correct. The
following sequence 01.
0.1
010.1
01.01
0101.01
010.101
01010.101
0101.0101
...
has the (improper) limit
((((((10^0)/10)+10^1)/10)+10^2)/10)+? = oo.
This implies the limit of the number of digits left to the decimal
point is the number of digits left of the decimal point of the limit,
namely larger than 0. And the limit of the set of digits left to the
decimal point is the same as the set of digits left to the decimal
point of the limit, namely {0, 1}, in particular it is not empty - in
contradiction with set theory.
Regards, WM
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