Virgil
Posts:
4,483
Registered:
1/6/11
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Re: Matheology � 162
Posted:
Nov 27, 2012 2:25 PM
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In article
<c16e876e-89fc-4e7f-83b7-4f8feae7e877@f17g2000vbz.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> 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. 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.
What is under discussion is which digit positions to the left of the
radix point eventually become and thereafter remain zero, and the answer
is all of them.
>
> In order to teach you the correct argument
Wm teaching anyone a correct argument? Pshaw!
> 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 it were true, one explanation would have been quite enough, but WM
does not seem to understand that repeating his false arguments, however
often, does not make them any less false.
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