Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
- From: tommy1729 <tommy1729@xxxxxxxxx>
- Date: Thu, 31 Jan 2008 18:37:19 EST
david C Ullrich wrote :
On Wed, 30 Jan 2008 13:11:03 EST, tommy1729
<tommy1729@xxxxxxxxx>
wrote:
Good summation methods usually manipulate thesequence of elements of the series or the partial
sums of the series.
since you dont agree on anything i ever say disprove that sentense david.
i dare you.
have been talking about. also changing rooms in
( as eg riemann series theorem ! )
(in other words : rearrangements !! as i and HdB
hilberts hotel)
actual limit on all convergent series.
A "regular" summability method agrees with the
and that last sentence here too, david , cmon disproof it.
is the most logical summability method.
therefore for divergent series analytic continuation
disproof this too, i dare you.
you doubted if i know what a summability method is.
ive pointed towards analytic continuation btw, but
And after reading this post it seems very clear that
you don't.
which makes me doubt if you know what analyticcontinuation is , btw ask anyone into theoretic
physics ;
summability method.
analytic continuation is STANDARD in physics as a
disproof that last sentence too david.
guess you cant hmm.
not needed) just compute the series as given.
if the series converges (if analytic continuation is
(or apply riemann series theorem if allowed todiscuss other values )
ha ! i talk about riemann series theorem for series that converge ; not diverge as you later here try to imply.
Let's see if I understand this. We have a divergent
series.
read agian i just said " if the series converges "
We want a
summability method that gives us some notion of what
the sum should
be taken to be in spite of the fact that the series
diverges.
And so we apply Riemann's theorem on rearrangements
as our summability
method?
ha ! another of your lies !
I just wrote : if the series converges !!
read again for the 3RD TIME !
You might note two things:
(i) Riemann's theorem talks about _convergent_
series, not divergent
series.
yes , read again for the 4TH TIME !!!
are going to keep up that stubbornness ?
i wrote : " if the series converges " !!!
So it's really hard to see the relevance in
the situation
above,
read again for the 5TH time
: "if the series converges..."
and before you start whining about more neccesary conditions : " if it applies " is also written.
where we're starting with a divergent series.
6TH already david.
which also means you at least lied 6 times about it.
Probably you
can explain that...
yes , youre lying , read for the 7TH time.
(ii) The theorem says that if a series is
conditionally convergent
then there is a rearrangement that converges to any
value we want.
Do you _really_ think that something that returns
"any value you want"
for an answer counts as a summability method?
Evidently you do, and
hence it _follows_ that you simply do not know the
_definition_ of
the phrase "summability method".
if the series is lacunary ( so no analyticcontinuation can be given ) most summation methods
fail most of the time( e.g. Borel ), thereby
strengthening the idea of analytic continuation.
disprove that last sentense david.
analytic continuation.
btw most summation methods give the same value as
and disproof that one too.
averaging.
many summation methods use special types of
disproof that too david.
or other (weird !! ) algebra such as :+ ...)
s = 1 + 2 + 4 + 8 + 16 + ... => s = 1 + 2( 1 + 2 + 4
so s = 1 + 2s => s = -1
That's not an example of a summabililty method.
then what is it ? it aint standard calculus or algebra because they would say = oo.
whereas others "just admit" the result is oo.summation method is.
***
i hope you realize now i do actually know what a
consistant in summability methods ( but wrong by a
and since weird algebra as above is considered
teacher of math learing a 14 years old convergence !
),
i see no reason to consider these things valid too :
"putting behind the ..." since it is no more
shameless manipulation from divergence to convergence
as 90 % of those crazy summation methods.
I didn't say anything about what you accept or what
you consider
valid. I don't see why anyone would care about that.
ha talk for yourself.
I've been
talking only about the question of whether you
understand
the meaning of the words you're using - over and over
you
demonstrate that the answer to that is no. Also
whether you
know the _statement_ of the theorem of Riemann that
you're
so obsessed about - the answer to that has been
clearly no
many times (the fact that you "consider" putting
terms
behinds the ... just as valid as something else has
no
bearing on the question of what the theorem actually
says.)
getting personal hmm ?
but you did lie about it , read again for the 8 TH time.
its not easy to say im wrong if you twist my words.
makes me wonder why you bother to copy at all, you just read what you want to read , not whats written.
you can get personal , but you havent disproven any statement i made.
and btw , you """ forgot """ to answer this challaging question below.
( "forgot" lol )
since your such an expert at everything :there is no analytic continuation and no equation as
what do you do when you have a divergent series and
above ( type s = f(s) )and you want a unique finite
result for your series by all the methods of
summation that still apply ( if some do ?! )
???thats the idea of me and HdB. ( and you dont accept
without putting behind the ... of course , since
that )
i wonder what your going to invent now.
nothing , just lies aparantly.
and no answer at all , not even an attempt.
weak david , very weak.
will you ever answer that question or ignore it forever ?
understand summability methods.
i do off course already know you wont admit i
Not as long as you _continue_ to _show_ that you
don't know the
_definition_ of the phrase, no.
well , why dont you give the definition of it and thus by that definition proof that :
riemann series theorem , borel summation , that equation i wrote , cauchy product , rearranging terms or the sequence of partial sums etc
are not summability methods at all.
btw all of this was already known by Riemann !
analytic continuation , his series theorem etc
regards
tommy1729
"Riemann, Matheyasevich and Wiles forever"
David C. Ullrich
dont be amazed david if others dont agree on your disproofs of the things i just challanged you to disproof.
your a very stubborn guy david.
i dont hate critics of what i just wrote, in fact i welcome them , but your not an honest one , you twist my words and dont admit the truth.
tommy1729
.
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