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

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 Carsten Schultz Posts: 4 Registered: 11/27/12
Re: Matheology § 162
Posted: Nov 27, 2012 1:52 PM

On 27.11.12 19:06, WM wrote:
> On 27 Nov., 14:15, Carsten Schultz <schu...@zedat.fu-berlin.de> wrote:
>
> The sequence (a_n) with
> a_n = (((?((((((10^0)/10)+10^1)/10)+10^2)/10)+? )+10^n)/10)
> has the (improper) limit infinity.
> Here we have an improper limit that, according to analysis, has
> infinitely many digits 1 left of the decimal point (i.e., a non empty
> set), and according to set theory the same limit has an empty set of
> digits left of the decimal point.

>>
>> 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!-

>
> Sorry, you are plainly wrong.

Oops, wrong example. What you complain about is that for

b(k,n) = 10^{k-n}, if n<=k<=2n, k odd,
b(k,n) = 0, otherwise

we have lim_{n->oo} sum_{k=0}^oo b(k,n)=oo even though
lim_{k->oo} b(k,n) = 0 for all n (and this is a limit of an eventually
constant sequence). Surely set theory must be to blame for this!

> Your well-known text book example does
> not yield a contradiction between analysis and set theory. The digits
> remain left of the decimal point (if there is any point at all). Only
> the positions of the digits =/= 0 cannot be determined in the limit.
> This is the same in analysis and set theory. And it is obviously not
> under discussion here.
>
> In order to teach you the correct argument I have explained it again
> above. Every person equipped with a minimum of intelligence should be
> able to understand it after the second explanation. If you have not
> yet understood it, feel free to ask again.
>
> Regards, WM
>

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