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Re: Matheology § 162
Posted:
Nov 27, 2012 8:15 AM
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On 27.11.12 09:37, WM wrote:
> On 27 Nov., 08:41, Virgil <vir...@ligriv.com> wrote:
>> In article
>> <aaa8416f-f069-4525-9261-406792ffb...@u9g2000vbm.googlegroups.com>,
>>
>>
>>
>>
>>
>> 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.
>>
>>
>>
>>> 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.
>
Mückenheim is worried by the fact that for a sequence (a_n)_n of
functions a_n: Z -> {0,1} it is possible that lim_{n->oo} a_n(k)=0 for
all k while the sequence sum_{k in Z} a_n(k) * 10^k tends to infinity
for n->oo. And of course he thinks that this is somehow set theory's
fault. What idiocy!
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