Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Matheology § 162
Replies: 78   Last Post: Dec 10, 2012 4:46 AM

 Messages: [ Previous | Next ]
 Carsten Schultz Posts: 4 Registered: 11/27/12
Re: Matheology § 162
Posted: Nov 27, 2012 8:15 AM

On 27.11.12 09:37, WM wrote:
> On 27 Nov., 08:41, Virgil <vir...@ligriv.com> wrote:
>> In article
>>
>>
>>
>>
>>
>> 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!

Date Subject Author
11/25/12 mueckenh@rz.fh-augsburg.de
11/25/12 Roland Franzius
11/25/12 namducnguyen
11/26/12 mueckenh@rz.fh-augsburg.de
11/26/12 Virgil
11/25/12 Virgil
11/26/12 mueckenh@rz.fh-augsburg.de
11/26/12 Virgil
11/26/12 mueckenh@rz.fh-augsburg.de
11/26/12 Virgil
11/26/12 YBM
11/26/12 mueckenh@rz.fh-augsburg.de
11/26/12 Virgil
11/27/12 mueckenh@rz.fh-augsburg.de
11/27/12 Virgil
11/27/12 mueckenh@rz.fh-augsburg.de
11/27/12 Carsten Schultz
11/27/12 mueckenh@rz.fh-augsburg.de
11/27/12 Carsten Schultz
11/27/12 Virgil
11/27/12 mueckenh@rz.fh-augsburg.de
11/27/12 Virgil
11/28/12 Carsten Schultz
11/29/12 mueckenh@rz.fh-augsburg.de
11/29/12 Virgil
11/27/12 Virgil
11/27/12 William Hughes
11/27/12 mueckenh@rz.fh-augsburg.de
11/27/12 William Hughes
11/27/12 mueckenh@rz.fh-augsburg.de
11/27/12 William Hughes
11/27/12 mueckenh@rz.fh-augsburg.de
11/27/12 Virgil
11/28/12 mueckenh@rz.fh-augsburg.de
11/28/12 Virgil
11/28/12 mueckenh@rz.fh-augsburg.de
11/28/12 Virgil
11/27/12 William Hughes
11/28/12 mueckenh@rz.fh-augsburg.de
11/28/12 Virgil
11/28/12 mueckenh@rz.fh-augsburg.de
11/28/12 Virgil
11/28/12 William Hughes
11/28/12 mueckenh@rz.fh-augsburg.de
11/28/12 William Hughes
11/28/12 mueckenh@rz.fh-augsburg.de
11/28/12 Michael Stemper
11/29/12 mueckenh@rz.fh-augsburg.de
11/29/12 Michael Stemper
11/29/12 mueckenh@rz.fh-augsburg.de
11/29/12 Michael Stemper
11/29/12 mueckenh@rz.fh-augsburg.de
11/29/12 YBM
11/29/12 trj
11/29/12 Virgil
11/30/12 mueckenh@rz.fh-augsburg.de
11/30/12 Virgil
12/1/12 mueckenh@rz.fh-augsburg.de
12/1/12 Virgil
11/29/12 Virgil
11/29/12 Virgil
11/28/12 Virgil
11/28/12 Virgil
12/10/12 veronika kočková
11/27/12 Virgil
11/27/12 YBM
11/27/12 Virgil
11/27/12 mueckenh@rz.fh-augsburg.de
11/27/12 Virgil
11/28/12 mueckenh@rz.fh-augsburg.de
11/28/12 Virgil
11/27/12 Virgil
11/27/12 mueckenh@rz.fh-augsburg.de
11/27/12 Virgil
11/28/12 Michael Stemper
11/28/12 mueckenh@rz.fh-augsburg.de
11/28/12 Virgil
11/29/12 mueckenh@rz.fh-augsburg.de
11/29/12 Virgil