what would euler do with
amy666
log(log(log(oo)))
seriously
log(oo) = 1 + 1/2 + 1/3 + ...
log(log(oo)) = 1/2 + 1/3 + 1/5 + ... ( 1/ primes )
but log(log(log(oo))) = ?
regards
tommy1729
Toni...@yahoo.com
**********************************************************************************
I think it is highly unprobable Euler would waste his time, and
others' as well, dwelling with nonsenses, leave alone with nonsenses
he doesn't even understand.
But who knows...? Perhaps in cold, remote St. Petersburg he had lots
of idle time...
Regards
Tonio
riderofgiraffes
Pubkeybreaker
> what would euler do with
>
> log(log(log(oo)))
>
> seriously
Nothing you say is serious......
>
> log(oo) = 1 + 1/2 + 1/3 + ...
>
> log(log(oo)) = 1/2 + 1/3 + 1/5 + ... ( 1/ primes )
>
> but log(log(log(oo))) = ?
I don't know what is happening in Tommy's fantasy world,
but someone intelligent might observe that since oo is not a
real number, that log(oo) is meaningless drivel, since the
domain of log() is (most usually) taken to be the positive reals.
log(oo) makes as much sense as log(cabbage).
And we don't need a snappy comeback that the the log function can
be applied to the complex numbers, because it is irrelevant here.
The domain here is not the Riemann sphere.
Go STUDY SOME MATH
amy666
antonio , you ignorant fool !
its not nonsense , in fact 90 % is a direct quote from euler itself !!!
haha , the critics of me make a fool of themselves again.
the more they want to have and show my ' nonsense ' the more ignorance BS they post themselves.
not even aware of the work of euler !
tommy1729
amy666
go study math ?
another ignorant fool unaware of the work of euler !!!
euler himself wrote :
log(oo) = 1 + 1/2 + 1/3 + 1/4 + ...
you critics make a fool of yourself instead of me !
tommy1729
amy666
thats bad math.
tommy1729
btw he probably said something different like
for all practical applications 0 =< log(log(log(n))) =< 3.
Denis Feldmann
Of course not. Show us the exact quote. Lets have all a good laugh.
Denis Feldmann
Where? Show us!
>
> you critics make a fool of yourself instead of me !
How long will it go on ? When will you learn? Anyway, dont worry for us...
>
>
> tommy1729
amy666
not exact but here is a good laugh !!
proof by euler = proof #1
on page
http://en.wikipedia.org/wiki/Proof_that_the_sum_of_the_reciprocals_of_the_primes_diverges
if your not blind you should have seen the log(log(+oo))
and if your really into math , you should have known this a long time ago.
so this proves it !!
and the fun is for me !!
hahahahaha
>
>
> >
> > haha , the critics of me make a fool of themselves
> again.
> >
> > the more they want to have and show my ' nonsense '
> the more ignorance BS they post themselves.
> >
> > not even aware of the work of euler !
> >
> > tommy1729
sci.math posters ; not even aware of the work of euler !
tommy1729
Toni...@yahoo.com
with things you don't understand which is a nonsense.
Tsk,tsk,tsk....you didn't EVEN understand that!
Regards
Tonio
> haha , the critics of me make a fool of themselves again.
>
> the more they want to have and show my ' nonsense ' the more ignorance BS they post themselves.
>
> not even aware of the work of euler !
>
> tommy1729- Hide quoted text -
>
> - Show quoted text -
amy666
where ?
where you snipped of course !!
cheater !
Dave L. Renfro
> I don't know what is happening in Tommy's fantasy world,
> but someone intelligent might observe that since oo is
> not a real number, that log(oo) is meaningless drivel,
> since the domain of log() is (most usually) taken to be
> the positive reals.
Not that I'm disagreeing with your main point, but I thought
I'd point out there are several old papers that have expressions
such as log(oo), sin(oo), etc. in them. I've encountered several
that were published before the JFM reviewing journal began
(around 1868), although I don't have the references with me
at the moment. However, using the JFM search page and using
google, I came up with the following. Some of these papers
I've also come across in library hardcopies of journal volumes,
and I believe I even have copies of the papers by Glaisher
and Walton at home somewhere.
These two have log(oo) in their JFM reviews (URL takes you to the
.pdf file of the review). I haven't checked the original papers
to see if log(oo) actually appears in either of the papers.
JFM 20.0258.01
Jamet, V.
Essai d'une nouvelle théorie élémentaire des logarithmes.
Title in English: A new elementary theory of logarithms
[J] Mathesis VIII. 40-44, 89-91.
Published: 1888
http://tinyurl.com/737mkd
JFM 33.0279.09
Reuschle, C.
Die allwertigen Ausdrücke $\frac 00$ etc.
[J] Math. naturw. Mitt. (2) 4, 17-29.
Published: (1902)
http://tinyurl.com/75wskc
The next paper uses sin(oo) and cos(oo) throughout.
The paper is freely available on the internet, in at
least two locations at google-books.
James Whitbread Lee Glaisher, "On sin oo and cos oo",
Messenger of Mathematics 5 (1871), 232-244.
http://books.google.com/books?id=89gLAAAAYAAJ&pg=PA232
http://books.google.com/books?id=MIsAAAAAMAAJ&pg=PA232
http://tinyurl.com/7juwpn [JFM review]
Glaisher's paper is mentioned in a footnote on p. 351 of
Alexander Freeman's 1878 English translation of Fourier's
"The Analytical Theory of Heat":
http://books.google.com/books?id=-N8EAAAAYAAJ&pg=PA351
Another paper that uses sin(oo) and cos(oo) is the following,
which is not on internet that I can find (the URL is for
it's JFM review).
W. Walton, "Note on sin oo and cos oo", Quarterly Journal
of Pure and Applied Mathematics 11 (1871), 326-327.
http://tinyurl.com/9ljudc
Finally, here are some other JFM reviews of papers in which
"sin oo" appears in the review. I haven't tried to see if
the expression actually appears in the papers themselves.
JFM 04.0139.02
Cayley, A.
Note on the integrals $\int_0^\infty\cos x^2dx$ and
$\int_0^\infty \sin x^2dx$.
[J] Quart. J. XII. 118-126.
Published: 1872
http://tinyurl.com/75fwve
JFM 15.0211.01
Johnson, W. W.; Judson, C. H.; Adcock, R. J.; Johnson, W. W.
Correspondence.
[J] Anal. X. resp. 44-46, 74-75, 89-90, 105-107.
Published: (1883)
http://tinyurl.com/9n7nnj
JFM 45.0374.02
Burkhardt, H.
II A 12. Trigonometrische Reihen und Integrale bis
etwa 1850.
[J] Enzykl. d. math. wiss. $II_1$, Heft 7, 819-1354.
Published: 1914
http://tinyurl.com/85pocu
Dave L. Renfro
quasi
So let that be a lesson to y'all -- once in awhile, tommy is actually
right!
Although, since those papers are mostly 1800s, perhaps tommy was just
placed in the wrong century!
quasi
Denis Feldmann
But I still dont see Euler writing it. Ok, I must admit I am a little
bit dishonest here (as the reference is actually in my personal
library, in this very good book (Euler, the master of us all ;you should
try to buy and read it))
So what? As if you were honest ...
And, of course, when Euler wtrites ln(ln(oo)), i is , in some xsense,
legal (not to mention that the standards at that time were lower than
they are now). When ou write it, you are just trynig to show off.
HAHAHAHAHA
>
> and if your really into math , you should have known this a long time ago.
I knew that the sum of inverses of primes diverges long before you were
born. A nice proof (adapted from Erdos) is on my website.
Mariano Suárez-Alvarez
The statement that tommy made means nothing without context,
which he did not supply. And one cannot be "right" when one
says meaningless things. Those equalities, I guess, are claims
regarding the asymptotics of ln n and ln ln n for large n.
But an equality such as
log(oo) = 1 + 1/2 + 1/3 + ...
means absolutely nothing, unless one specifies how n grows,
in what sense the asymtotics are being taken, and so on.
It may be the case that Euler wrote precisely that formula,
but he and his readers had a certain set of conventions in
mind which provided the context.
-- m
Matt
> what would euler do with
>
> log(log(log(oo)))
>
> seriously
>
> log(oo) = 1 + 1/2 + 1/3 + ...
>
> log(log(oo)) = 1/2 + 1/3 + 1/5 + ... ( 1/ primes )
>
> but log(log(log(oo))) = ?
Even though this formulation is imprecise and somewhat peculiar, it
seems to me that there's the bones of an interesting question here.
quasi
Granted.
But it's clear that providing context is not one of tommy's strong
points. Most of the context is private data, visible only to tommy or
to those with special decoder glasses.
However my claim that "once in awhile, tommy is actually right!" still
holds (or at least would be hard to disprove).
quasi
Denis Feldmann
*integers* such that q_n ~ n log n (log log(n)), ie almost as dense as
primes. I dont know of any good one ; do you ?
Mariano Suárez-Alvarez
It would be very hard to disprove a claim such as "somewhere
in the universe, four pink elephants are playing bridge
while drinking Darjeerling oolong and casually talking
about their short term financial perspectives" also... ;-)
-- m
Toni...@yahoo.com
wrote:
>
> > if your not blind you should have seen the log(log(+oo))
>
> But I still dont see Euler writing it. Ok, I must admit I am a little
> bit dishonest here (as the reference is actually in my personal
> library, in this very good book (Euler, the master of us all ;you should
> try to buy and read it))
>
> So what? As if you were honest ...
>
> And, of course, when Euler wtrites ln(ln(oo)), i is , in some xsense,
> legal (not to mention that the standards at that time were lower than
> they are now). When ou write it, you are just trynig to show off.
>
> HAHAHAHAHA
>
>
>
> > and if your really into math , you should have known this a long time ago.
>
> I knew that the sum of inverses of primes diverges long before you were
> born. A nice proof (adapted from Erdos) is on my website.
>
Salute, mon ami! Could we have a link to that site of yours, please?
Thanx
Regards
Tonio
quasi
Granted.
But it's clear that providing context is not one of tommy's strong
points. Most of the context is private data, visible only to tommy or
to those with special decoder glasses.
However to be fair, he did eventually at least give a glimpse of his
intended context (Euler, primes, convergent series).
In any case, my claim that "once in awhile, tommy is actually right!"
still holds (or at least would be hard to disprove).
[Note -- I posted this earlier but it apparently didn't go through.]
quasi
Matt
wrote:
It is the sum of the reciprocals of the primes <= n that tends to log
(log(n)), right? I'm slightly confused because some references give
results such as Sum k=1^n 1/p_k = log(log(n)) + ..., which to me means
the sum of the reciprocals of the first n primes...
amy666
but i specificly mentioned euler ...
so that is the context ...
and people should know the work of euler if they claim to be mathematicians.
so no decoders needed.
regards
tommy1729
Mariano Suárez-Alvarez
> quasi wrote :
>
>
>
> > On Wed, 14 Jan 2009 09:56:28 -0800 (PST), Mariano
> > Suárez-Alvarez
Anyone who's seen the many volumes which comprise Euler's
Oeuvre clearly knows that saying "Euler" is giving as much
context as saying "Earth" is giving directions to get to
my house.
-- m
David R Tribble
> log(oo) = 1 + 1/2 + 1/3 + ...
> log(log(oo)) = 1/2 + 1/3 + 1/5 + ... ( 1/ primes )
>
> if your not blind you should have seen the log(log(+oo))
> and if your really into math , you should have known this a long time ago.
> so this proves it !!
You must have missed this part in the Wiki article:
It is almost certain that Euler meant that the sum of the
reciprocals of the primes less than n is asymptotic to
ln(ln(n)) as n approaches infinity. It turns out this is
indeed the case; Euler had reached a correct result
by questionable means.
Matt
Well, it must be the former, I guess...
Maybe a sequence something like Sum i=2^oo 1/f(i) where f(i) = floor
(sum_j=2^i log(j)*log(log(j))) would work (I'm not 100% confident),
but even if true that's not in this context a "good" sequence by my
reckoning. We need something like "super-primes" that have a pleasing
and relevant construction and the correct asymptotic density.
Denis Feldmann
Sure : http://denisfeldmann.fr (the math section is at
http://denisfeldmann.fr/maths.htm , and for instance the proof above is
at http://denisfeldmann.fr/PDF/erdos.pdf ) Alas, the main bulk of it is
in French...
Denis Feldmann
Both are true :-) in the first case, we get sum (k<n/ln (n)) 1/klog k ~
log log (n/log n) ~log log (n)...
Michael Press
quasi <qu...@null.set> wrote:
> On Wed, 14 Jan 2009 09:56:28 -0800 (PST), Mariano Suárez-Alvarez
> <mariano.su...@gmail.com> wrote:
>
> >On Jan 14, 2:44 pm, quasi <qu...@null.set> wrote:
[...]
> >> So let that be a lesson to y'all -- once in awhile, tommy is actually
> >> right!
> >
> >The statement that tommy made means nothing without context,
> >which he did not supply. And one cannot be "right" when one
> >says meaningless things. Those equalities, I guess, are claims
> >regarding the asymptotics of ln n and ln ln n for large n.
> >But an equality such as
> >
> > log(oo) = 1 + 1/2 + 1/3 + ...
> >
> >means absolutely nothing, unless one specifies how n grows,
> >in what sense the asymtotics are being taken, and so on.
> >It may be the case that Euler wrote precisely that formula,
> >but he and his readers had a certain set of conventions in
> >mind which provided the context.
>
> Granted.
>
> But it's clear that providing context is not one of tommy's strong
> points. Most of the context is private data, visible only to tommy or
> to those with special decoder glasses.
>
> However my claim that "once in awhile, tommy is actually right!" still
> holds (or at least would be hard to disprove).
Tommy1729/amy666 is contentious and does not present
cogent mathematical arguments. Finding a correct statement
in tommy1729/amy666's writings is the same as seeing an
elephant in a cloud formation. Q.E.D.
--
Michael Press
Denis Feldmann
http://en.wikipedia.org/wiki/Meissel-Mertens_constant) will not be the same
Matt
wrote:
> Matt a écrit :
>
>
>
>
>
> > On Jan 14, 7:33 pm, Denis Feldmann <denis.feldmann.sanss...@neuf.fr>
> > wrote:
> >> Matt a écrit :> On Jan 13, 11:49 pm, amy666 <tommy1...@hotmail.com> wrote:
> >>>> what would euler do with
> >>>> log(log(log(oo)))
> >>>> seriously
> >>>> log(oo) = 1 + 1/2 + 1/3 + ...
> >>>> log(log(oo)) = 1/2 + 1/3 + 1/5 + ... ( 1/ primes )
> >>>> but log(log(log(oo))) = ?
> >>> Even though this formulation is imprecise and somewhat peculiar, it
> >>> seems to me that there's the bones of an interesting question here.
> >> To stay in the spirit, you would need to find a sequence q_n of
> >> *integers* such that q_n ~ n log n (log log(n)), ie almost as dense as
> >> primes. I dont know of any good one ; do you ?
>
> > It is the sum of the reciprocals of the primes <= n that tends to log
> > (log(n)), right? I'm slightly confused because some references give
> > results such as Sum k=1^n 1/p_k = log(log(n)) + ..., which to me means
> > the sum of the reciprocals of the first n primes...
>
> Both are true :-)
Oh! I didn't realise. Thank you.
amy666
no i didnt.
when talking about euler , i use euler notation.
just like we use zeta(s) instead of zeta(x) or zeta(z) because riemann used s.
as for the questionable that depends what you mean by questionable.
wikipedia probably refers to the sloppy notation and weak proof.
there are nicer proofs , also with stricter bounds.
but euler is euler and there was no other euler.
and most proofs are based on eulers proof anyways ( at # 2 is probably erdos )
its funny how some people change the story of their ignorance of euler to the assumed ignorance of the one talking about euler ...
regards
tommy1729
amy666
but euler is more famous than paris.
especially to real mathematicians.
its like you claim to be an expert on your house and visit it everyday.
but still you need directions after taking out your dog around the block.
besides , sure euler wrote a lot , but this part is one the most famous thus a real mathematician should know about it.
regards
tommy1729
amy666
nonsense.
you have some guts , since quasi has seen some proofs of me about number theory.
we have been discussing many polynomial issues in which both my proofs and conjectures were intresting.
quasi math was good too and a few others ( galathaea , robert israel , dave l renfro , tim , adler , ... )
were were the critics in those threads ?
absent !!
pretend it never happened ... just like press is doing right now.
when i have a conjecture :
no disproof or proof given ; any fool can make a conjecture
when i have a proof :
ignore it.
when i have question :
point out that i dont have an answer or proof
that poor strategy is so easily recognizable , its pathetic.
i could just do the same with the posts of my critics.
since if you dont value conjectures , proofs nor questions/new ideas/concepts then basicly you could redicule any post by any poster.
but that doesnt make you a better mathematician.
> Q.E.D.
>
> --
> Michael Press
hasnt learned his lesson ...
regards
tommy1729