Re: 1-1/2+1/3-1/4+1/5-1/6+1/7

On Thu, 31 Jan 2008 18:37:19 EST, tommy1729 <tommy1729@xxxxxxxxx>
wrote:

david C Ullrich wrote :

On Wed, 30 Jan 2008 13:11:03 EST, tommy1729
<tommy1729@xxxxxxxxx>
wrote:

Good summation methods usually manipulate the
sequence 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.

Huh? That sentence is true - why would you imagine
I thought it was false.

This is simply pathetic. You say a lot of false things. When
you say something false someone usually points out that
it's false. The reason that happens so often is not that people
feel some need to show that everything you say is wrong,
the reason people contradict you so much is that so many
of the things you say _are_ wrong.


( as eg riemann series theorem ! )

(in other words : rearrangements !! as i and HdB
have been talking about. also changing rooms in
hilberts hotel)

A "regular" summability method agrees with the
actual limit on all convergent series.

and that last sentence here too, david , cmon disproof it.



therefore for divergent series analytic continuation
is the most logical summability method.

disproof this too, i dare you.



ive pointed towards analytic continuation btw, but
you doubted if i know what a summability method is.

And after reading this post it seems very clear that
you don't.

which makes me doubt if you know what analytic
continuation is , btw ask anyone into theoretic
physics ;

analytic continuation is STANDARD in physics as a
summability method.

disproof that last sentence too david.

guess you cant hmm.



if the series converges (if analytic continuation is
not needed) just compute the series as given.
(or apply riemann series theorem if allowed to
discuss 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 "

Yes, you said if the series converges just compute the value.
If the series converges then the whole notion of summability
methods simply doesn't come up - we need summability
methods for _divergent_ series.

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 !

[...]


(ii) The theorem says that if a series is
conditionally convergent
then there is a rearrangement that converges to any
value we want.

You didn't answer the following, by the way:

Do you _really_ think that something that returns
"any value you want"
for an answer counts as a summability method?

Do you? And do you really think that "any answer you
want" is a _useful_ answer when we have a divergent
series that we're trying to interpret somehow?

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 analytic
continuation 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.



btw most summation methods give the same value as
analytic continuation.

and disproof that one too.



many summation methods use special types of
averaging.

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 ?

Fascinating. You _still_ don't know the definition of
"summability method".

it aint standard calculus or algebra because they would say = oo.



whereas others "just admit" the result is oo.

***

i hope you realize now i do actually know what a
summation method is.

and since weird algebra as above is considered
consistant in summability methods ( but wrong by a
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 ?

Huh?

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.

You said that Riemann's theorem said that if you have a series with
infinitely many positive terms and infinitely many negative terms then
it can be rearranged to give any value you want. Many people including
me have given counterexamples to that.

and btw , you """ forgot """ to answer this challaging question below.

( "forgot" lol )




since your such an expert at everything :

what do you do when you have a divergent series and
there is no analytic continuation and no equation as
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 ?! )
???

I didn't answer the question because it's not a mathematical
question as stated. What do you mean, "what do I do when
I have a divergent series and I want a unique finite result"?
I _don't_ "want" results - what I do depends on what I'm
trying to accomplish. For example, various summability
methods are useful substitutes for convergence in Fourier
analysis - when I can _prove_ that a certain summability
method does what I'm trying to do I use it.

without putting behind the ... of course , since
thats the idea of me and HdB. ( and you dont accept
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 ?



i do off course already know you wont admit i
understand summability methods.

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

Because it's much more fun to watch you continue to make an
idiot of yourself by using the term in totally inappropriate ways.

(People who like to defend underdogs should note: If he was
talking about something he brought up himself and used the
phrase "summability method" to mean something that's not
quite a summability method that would be no problem. But
here it's different: Feldman was asking about summability
methods, _using_ the term in its standard sense, when he
*** in expostulating about how we're all ignorant of
riemann's theorem.)

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.

Why do you ask me to prove so many things that I've never claimed were
true?



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.

Giggle. You haven't noticed that when people speak up they _do_ agree
with my disproofs of things you say? You haven't been paying attention
I guess.

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

David C. Ullrich
.

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