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Re: Matheology § 162
Posted:
Nov 27, 2012 3:37 AM
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On 27 Nov., 08:41, Virgil <vir...@ligriv.com> wrote:
> In article
> <aaa8416f-f069-4525-9261-406792ffb...@u9g2000vbm.googlegroups.com>,
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>
>
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> WM <mueck...@rz.fh-augsburg.de> wrote:
> > On 26 Nov., 20:55, Virgil <vir...@ligriv.com> wrote:
>
> > > > There are not different topologies involved when calculating sets of
> > > > digits of analytical limits. Nevertheless even you seem to be capable
> > > > of recognizing that set theory is not suitable for calculating limits
> > > > of analysis.
>
> > > While "different topologies" may be overstating the case, differing
> > > situations is not.
>
> > > WM compares a sequence of supposedly real numbers and a sequence of sets
> > > of digit positions, and says that because the limits of such different
> > > sequences can be different that mathematics has failed.
>
> > You have not yet understood. I compare the analytical limit of a
> > sequence of digits positions and the set theoretic limit of the same
> > sequence of digit positions.
>
> I understand that you compare apples to oranges and are unhappy to find
> they are different.
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> > The analytical limit is obtained via (x --> oo) ==> (logx --> oo) from
> > the limit of the sequence of real numbers, but does that invalidate
> > the analytical mathod?
>
> Anyone who needs "(x --> oo) ==> (logx --> oo)" to compute the
> analytical limit of WM's sequence of reals
Again you misunderstand. This relation is not needed to compute the
analytical limit of reals but to compute the set of indexed digits
left to the decimal point, or, as you call it, the limit of the
sequence of sets of positions left of the radix point.
>
> But however that limit is reached, it has nothing to do with the limit
> of the sequence of sets of positions left of the radix point having
> non-zero values, which limit is the empty set.
The set of indexed digits left to the decimal point, or, as you call
it, the limit of the sequence of sets of positions left of the radix
point, is not empty - according to analysis.
According to set theory the limit set is empty. This is a
contradiction of analysis and set theory.
Regards, WM
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