Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: tommy1729 <tommy1729@xxxxxxxxx>
- Date: Thu, 17 Jan 2008 18:14:02 EST
David wrote :
On Wed, 16 Jan 2008 15:56:29 EST, tommy1729
<tommy1729@xxxxxxxxx>
wrote:
1-1/2+1/3-1/4+1/5-1/6+ ....
this series can be made to sum to anything.
The way you phrase this is meaningless - you
mean that it can be made to sum to any real
number just by rearranging the order of the terms.
Yes, that's true. We all know that. Nobody
has denied that.
lol !!
you are the person who denied this in the beginning !!
( possibly together with your friend dave seaman )
that is the very reason i got so angry and started some new threats.
What people have denied is something you said that
was not true: That any divergent series with
infinitely
many positive terms has the same property.
only partly true, for starters also this condition :
1) also infinitely many negative terms.
in fact i claimed " Riemann's Series theorem to apply to 1-1/2+1/3-... " and thus that series can be made to sum to anything ( real number ).
and this is true.
yet you said i was wrong and insulted me ( as usual )
typical.
apparently most of you dont understand hilbert'shotel
however you dare too claim that i dont !!
but you are the one confused !
No, when you give an example of a "rearrangement"
that involves taking an infinite subset first
and then adding more on it's clear that you're
missing the point.
what point do you refer too ?
i got the point where you said i was wrong and an idiot and now (?) you admit the series 1 -1/2 +1/3 -1/4 + ... can indeed be summed to anything (real number).
so i got angry and started a few threads.
...
and you still dont admit your mistake.
and never will.
despite Riemann's Series theorem AND Hilbert's hotel are correct and APPLY to series rearrangements AND terms are indeed reordered AND this applies to the series 1 -1/2 +1/3 - 1/4 + ... AND with or without accepting ZFC / PST / TST / ANY set theory !!!
and i have not even begun to include cauchy products multisections and other more advanced tools.
if you understand so well answer this simplequestion :
elements.
N = [0,1,2,3,4,5,...]
"Square" = [0,1,4,9,16,25,36,...]
notice the " point to point correspondance "
now the set containing N but not "Square" is L
rearrange the set N : containing both L and "Square"
called T.
this set contains all non-negative integers and is
count oo long for the squares and thus the limit of
T = [0,1,4,9,16,25,...,2,3,5,6,7,8,10,...]
now since the "one to one correspondance" we can
our series can skip the non-square elements.
position does 2 occur in the set T ?
still dont believe it ?
than answer the simply question : at what finite
admit i am correct.
if you answer oo ; thats not finite , and thus you
and you can give this finite number !
...
else im curious what number you will come up with
its another series "skipping elements" method ,
as for Riemann's series theorem : just admit it ;
similar and justified by Hilbert's hotel.
value of a series , since if you dont , there is
"skipping elements" is the only way to choose any
divergence as in :
different series.
1-1+1-1+1-1+...
or you use analytic continuations which are actually
or you hide the skipping in a subtle multisection.
the principle is so simple.
you are confused ; not me.
************************
David C. Ullrich
( slightly off topic : )
Riemann beats the **** out of cantor.
his concept of infinity is much better.
and he was well aware of the difference between aleph_0 and aleph_1 , he probably called it dense and continu or something like that.
( measure theory was also known to him , and also fourrier series SO he must have know the distinction )
and as someone recently posted ; Riemann's Series theorem is much stronger and general than believed.
and there are no " russel-type paradoxes " or the need for "ZFC- type axiom references to support his ideas , what he did not even do himself" as do exist for cantor's ideas.
regards
tommy1729
.
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