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5:00 PM
@Ropstah RH has a prime variant of it, but why should that mean it is based on primes?
 
Can someone explain what you guys are doing with the functions? (i got ChatJax, but I can't seem to follow in terms of metainformation)
because zero's are calculated based on the log calculations relative to primes?
 
@Ropstah huh?
 
I saw an explanation on youtube with made a table:

log(x) | log(y) | log(z) etc... producing + or - or 0
based on primes
 
these + / - and 0 values were used to calculate Riemann's zero's
 
5:02 PM
anything on youtube might just be a bunch of bullcrap, but I'll try to see what it says nevertheless.
what do you mean by log(x) | log(y) | ...?
 
Von Mangoldt
 
yes?
 
Append: #t=2494
to the url
 
sorry my internet is too slow for that. i think you are confusing two things.
primes can be calculated with the help of zeta zeros, not the other way
 
I get that
How are zeta zero's calculated? Isn't Von Mangoldt involved there?
 
5:05 PM
I derived a short algorithm for calculating first 100 zeta zeros on the half line in here.
have a look if you are interested.
 
@BalarkaSen: Please see: tinypic.com/r/fneqdk/8
 
@BalarkaSen @Hippalectryon it is possible to express the integral in terms of harmonic numbers. But how?
 
@Ropstah When he said what is the relationship between 26 and 39 so many people muttered that they were prime ... :P
 
@Ropstah i can't see it. maybe my internet is too slow.
 
Am I the only one here who doesn't understand what is going on?
 
5:08 PM
@BalarkaSen: Does this work: oi62.tinypic.com/fneqdk.jpg
@Moron: No i don't understand either :)
 
nope
 
I'm so stupid haha, can upload here
 
@Ropstah Glad.
 
@BalarkaSen: I meant that waveform
 
wait a sec it's taking time to load.
but it's loading nevertheless.
 
5:10 PM
:)
 
@Ropstah That's just a naive, very, very naive form of RH. One has to define what one means by "random" =P.
 
But am I naive in comparing it to my waveform?
"my"
 
What is that?
 
Distribution of pseudoprimes under 1.000.000
Fibonacci
However, different list than others produce
 
Well, primes are (semi)randomly distributed, so I believe that is (semi)random as well.
 
5:13 PM
How to prove that an inductively defined sequence ( e.g. $x_1 = 1 , x_{n+1} = 3.x_n²$ )is unbounded by induction ? Somehow, trying to prove the definition of unboundedness ( "$x_n$ is unbounded above iff for all c in R , there exists $n_0$ with $ n>n_0 \to x_n > C$ " ) doesn't work for inductively defined sequences.
 
Yes it is i think
Can you explain how the naive naive form of RH displayed above is furtherly defined in terms of those waveforms displayed?
Are they still used in the basis of the theorem?
Or in other words, can the waveform be replaced by a different waveform in turn altering the results of the hypothesis?
 
@nerdy Why don't you try to arrive at a contradiction after assuming that the sequence is bounded.
 
i was curious on how to prove directly by induction
that it is unbounded
 
@Ropstah i am not sure if your waveform is related to RH, though
 
@nerdy What is your inductive hypothesis?
 
5:16 PM
I'm sure it probably isn't by now, but I want to make sure
Does my last question make sense? In being at the base of the theorem?
 
well, what do you really mean by "waveforms"? they are just a bunch of random walks, aren't they?
 
x1=1,xn+1=3.xn² is unbounded above for all n>=1
so, to prove that, i want to show it is unbounded above for n=1
 
yes excuse me, me talking in waveforms is wrong, i mean the diagram produced which is seemingly random (Mobius, Von Mangoldt)
 
I don't think there is an inductive proof for that.
 
@Ropstah the connection of random walks (waveforms, as you say) with RH are very, very naive in one sense and the closest probably is Denjoy's interpretation. It says that Riemann hypothesis is true with probability 1 if $\mu(n)$ behaves like a random variable for very large $n$s, so RH is really related to randomness of distributions of square-free numbers rather than primes.
I have written it up in here
 
5:23 PM
back
 
I'm indeed looking for certain kinds of probability. These probabilities are subject to a certain error percentage right?
 
Moron, if you give me a real number C, if the sequence is explicitly defined, i can try to give where ( an index ) the sequence becomes greater than that
but if the sequence is inductively defined, i don't know how to give you such index
 
i don't think so. probabilistic interpretations can hardly be rigorized, @Ropstah
 
that is my problem
 
probability is just probability and hard-core estimations are just hard-core estimations.
 
5:27 PM
@BalarkaSen: Maybe in short: does it make sense to compare the Fibonacci pseudoprimes to prime distribution theorems?
 
@Ropstah i don't see why you are bothering with Fibonacci pseudoprimes. there are a whole bunch of strong pseudoprime tests out there and each of them are as good as Fibonacci. pseudoprimes in some sense do sieve out a bunch of composites but they are never really of theoretical interest. anyway, i dunno.
 
@BalarkaSen @Hippalectryon Does it make sense? $$\int_0^1 x^n \log(1+x) \ dx=\frac{1}{n+1}\left(H_{n+1}-H_{(n+1)/2}\right)$$
 
@BalarkaSen: I'm fascinated by the fact that all primes come out of this easy method, but a small subset of numbers (getting smaller and smaller) are not prime
 
Moron , i just figured it out
we can prove that it is strictly greater than an unbounded sequence
and conclude that must be also unbounded
 
Besides that, I don't understand why my implementation generates more numbers than other algorithms
(a few more)
 
5:31 PM
@Chris'ssis Uh how can I know
 
i'm prepared to bet that there exists better algorithm than yours.
 
Yes, much better
It's dead simple, but uses GCD() which makes no sense from a computational point of view
 
@Ropstah How many composites do your algorithm return upto 1000?
 
Who flagged me just now? I was suspended again, lol.
 
@WillHunting What did you say? :-)
 
5:34 PM
@BalarkaSan: These aren't composites perse, but it returns this:1
5
323
377
442
 
@Chris'ssis I said "If you can't sleep, sleep with someone", lol.
 
wait
 
@WillHunting Can you be suspended for this, automatically?
 
@BalarkaSen: haha, please read adjusted message
 
@Ropstah what are those?
 
5:35 PM
@Chris'ssis I think enough people agreed that it was bad, so I got suspended. Well, well, looks like it is getting easier to be suspended nowadays.
 
First numbers produced under 1000
These numbers are produced by the algorithm but are NOT prime
 
aha, so these are the composites sneaking out.
 
@WillHunting Then I should be careful with my questions, some here might like to suspend me for my questions. :-)
(like @PedroTamaroff)
 
Well, 1 and 5 not being composites?
Ah, these are primes but NOT generated by the algorithm, my bad
 
@Chris'ssis Yes, I am a freedom hater.
2
 
5:37 PM
I'm checking predition != real
 
I am a freedom fighter!
 
I am in leagues with @Pedro
 
@WillHunting By the way, did you begin going jogging every day?
 
5:38 PM
And next, 442 (and 2834 for that matter) are obviously not prime due to %2. But the algorithm produces those (only those are even)
 
@WillHunting Wait, let me flag you for saying 'Hi'
 
@Chris'ssis I am only walking this month, I will start jogging next month.
 
@WillHunting lolll, it's always the next week, month, year ... :-)
 
@IceBoy Like a firefighter, but with freedom. Yes.
 
@IceBoy Like fire fighters fight fire?
 
5:39 PM
Me too.
@DanielFischer HA! High five!
 
@DanielFischer +1
 
Hola @PedroTamaroff. Make it ten :D
 
@DanielFischer I match your 10 and raise it to 20.
 
I'm ALL in
 
folds all 50 fingers
 
5:41 PM
@BalarkaSen Fold your other hand too !
 
lays down hand Two thumbs and a dweezil.
 
user116848
@Mitch What's a dweezil? :-)
 
About 3 pounds!!!!!!
 
user116848
I see
 
What do you guys think of this:
http://embed.plnkr.co/jNA28BBb2JFAccPPX61p/preview

Not meant for die hard ascii coders, but this is kind of osx/ios style, symbol input, but then for math use.
 
user116848
5:44 PM
@IceBoy hi :-)
 
@Arrowfar It's an odd extra toe.
 
@Arrowfar hi
 
Hi!
 
user116848
@Mitch This is the first time I have the word.
 
Dweezil Zappa (born September 5, 1969) is an American rock guitarist and occasional actor. He is the son of musician Frank Zappa. == Early life == Zappa was born in Los Angeles, California, the son of musician Frank Zappa and Gail Zappa, who worked in business. He is the second of four siblings: his older sister, Moon, younger sister Diva and younger brother Ahmet. He is the cousin of actress Lala Sloatman. Zappa's father was of Sicilian, Greek, Arab, and French descent, and his mother was of French, Irish and mostly Danish ancestry. Dweezil's registered birth name was Ian Donald Calvin Euclid...
 
5:47 PM
@Arrowfar He is an Eng SE user.
=P
 
They came in to see what is flagged here.
 
@BalarkaSen and what's wrong with that?
 
He would use words no one ever even heard of.
 
icic
good point
 
@robjohn I'm very curious to find what $A(n)$ and $B(n)$ are in $$\int_0^1 x^{2n-1} \log(1-x) \log(1+x) \ dx =A(n)-B(n) \log(2) $$ At the moment it's a mystery.
 
5:50 PM
in English Language & Usage, 7 hours ago, by Robusto
A word that nobody will understand is helpful to whom, exactly? — Robusto 43 secs ago
 
@BalarkaSen: Going back to the theoretical interest of pseudoprime tests. You say there isn't any theoretical interest whatsoever? Is that because of the errors?
 
@Ropstah More or less.
 
@BalarkaSen Isn't it interesting that a seemingly unstructured sequence like the prime numbers is generated with less and less errors by a structured sequence like the fibonacci numbers?
 
@BalarkaSen I've never heard of it!
 
@Ropstah Nope. It's easy to approximate n-th primes, for example.
 
5:53 PM
I understand, however it also produces distribution
below the nth prime... or is that the caveat?
 
It just approximates it.
There are lots of such approximations.
 
Fair enough, but the approximation becomes better as the values increase
 
That's what we call "asymptotic approxes"
 
@BalarkaSen: Let me explain where my head is going, please tell me that i'm wrong
Fibonacci is based on Pythagoras, introducing sqrt(5)
Being based on a rectangular system with angles of 90 degrees, 45 degrees and after that producing decimal degrees
Is there a Pythagoras equivalent in triangular space (producing pyramids instead of cubes) where Fibonacci produces different results?
 
I've formulated a simple theorem which is likely to be true. I want to find its shortest possible proof. Is it OK to ask it at math.SE even despite I can solve it myself with a little work?
 
5:57 PM
Being able to work with: 60 degrees, 30 degrees, 15 degrees
 
@Ropstah yes, there is.
 
base-3?
 
what do you mean by that?
 
Is the answer 'naively' speaking: base-3?
Or is it more advanced like: en.wikipedia.org/wiki/Pythagorean_tuning
 
5:59 PM
would this qualify as a generalization, for example
 
Is that concept related to Pythagorean tuning?
 
i dunno what that is. why don't you click the link and see for yourself?
 
I'm reading it really :)
@BalarkaSan: Where I got so far combining geometry and numerology (Euclid?): 10^2 makes a square (2 dimensional), whereas 10^2 (squaring) in base 3 creates a pyramid (3 dimensional)
 
So, we ought to have that $$\sum_{n=1}^{\infty} \frac{1}{n}(A(n+1)-B(n+1) \log(2))=3\log(2)-\log^2(2)-\frac{3}{4}$$
 
@BalarkaSen: I hadn't seen "De Gua" yet. Is that the theorem which I should look further into?
 
6:07 PM
it's just pitagoras for 3-simplex
 
It basically involves calculating volume, am I correct?
 
no, just area.
 
Instead of area
Hmm
"This theorem is essentially the inner-product-space version of Pythagoras’ theorem applied to the kth exterior power of n-dimensional Euclidean space. "
 
oh if you mean volume = area^2 then definitely volume
 
That makes it a cube again right? Not handling the 'pyramid' shape
Triangular cylinder?
 
6:10 PM
i don't see what you're trying to say
oops i have to run.
 
Maybe not
me neither :)
 
sorry
 
THanks so far
Me too, have to keep eating and so on
 
@DanielFischer Dini ?
 
Talk to you later hopefully!
 
6:12 PM
@DanielFischer ah, seems like I didn't know about Monotone Convergence Theorem for Series
 
@G.T.R A series is just an integral with respect to the counting measure. That often helps. (The proofs for series are usually simpler, but one often is more used to the techniques for integrals.)
 
@BalarkaSen: that will be on the fact that the tetrahedron has to be equilateral in terms for it to work as 'whole' number and for it to fit in certain cubes again
 
6:28 PM
how can I prove that P <-> Q = (P -> Q) /\ (Q -> P)? I can write out the implications but then I'm completely stuck. Any pointers on where to proceed?
 
@Chris'ssis I assume they're supposed to be rational...
 
Why this question was counted offtopic? math.stackexchange.com/questions/927856/…
 
@robjohn Yeah.
 
what is so special about having the shortest proof?
other than length :-)
 
@IceBoy: I want the shortest proof in the book I am writing
 
6:34 PM
is your book entitled "the shortest proofs"?
 
@Chris'ssis What's $\sum_{k=1}^\infty\frac{1}{k+\ln(n)}$ ?
 
$\infty$
 
1 over k plus natural logarithm of n
 
@Hippalectryon What do you expect me to say it is?
 
6:43 PM
And what is $\sum_{k=1}^\infty\frac{1}{k+\ln(k)}$ when $k$ does not have $7$ in its decimal form ?
@Chris'ssis Idk how to find that ^ one
 
natural logarithm being base 9?
 
No
I mean
It's the sum for k=1,2,...,6,8,...,16,18,..(...)...,69,80,81,....
 
@Hippalectryon These questions are classical, I have some in my books.
 
@Chris'ssis What is classical is the convergence of the sum
 
What does it mean 'not having a certain digit in decimal form'?
 
6:45 PM
But I have been unale to find the limit
@Ropstah For instance, 12358645 does not have 7
but 154564564 7 521 does
 
ah right, so just base 10 but not using 7 anywhere
 
What does this sort of problem relate to?
Conceptually?
 
@Ropstah This look like a homework problem, not a real problem
 
It's just a twist on kempner sums
 
6:47 PM
Ah ok, purely theoretical
 
The Kempner series is a modification of the harmonic series, formed by omitting all terms whose denominator expressed in base 10 contains a 9 digit. That is, it is the sum where the prime indicates that n takes only values whose decimal expansion has no 9s. The series was first studied by A. J. Kempner in 1914. The series is interesting because of the counter-intuitive result that, unlike the harmonic series, the Kempner series converges (Kempner showed this value was less than 80 and Baillie showed that to 20 decimals, the actual sum is 22.92067 66192 64150 34816 (sequence A082838 in OEIS))....
 
@Hippalectryon When I finish this one math.stackexchange.com/questions/925092/… then I do any sum you want to.
(working on it hardly)
 
@Chris'ssis Don't forget :)
 
@Hippalectryon No :-)
 
@Chris'ssis: Is a tesseract hypergeometric?
As in hypergeometric compared to cube
Or is it hypergeometric as in pyramid compared to cube?
Or none of the above? haha
 
6:50 PM
@Ropstah No
 
Fair enough
 
@Chris'ssis You probably meant "hard" instead of "hardly".
 
@DanielFischer You should have told me a bit faster. ;)
 
Another night work coming up: youtube.com/watch?v=BCeFgnh6A1U
 
@DanielFischer Actually there is a big difference between hard and hardly. I'll keep this in mind. Thanks.
 
6:54 PM
@Chris'ssis Yes, that's an insidious trap for non-native speakers.
 
@DanielFischer Perhaps the next English book I should read must be about traps in English language.
 
there are a lot of insidious traps :-)
 
@IceBoy the risks of autodidacticism
 
true
 
@IceBoy The same thing with study and learn. Some don't make the difference.
One can study a lot, but learn nothing (theoretically).
 
7:06 PM
yes, it does matter what one means by "learn" :-)
I had this argument today in the english room :-/
our definitions differed
this ultimately comes down to one's philosophy
or opinion
"Education is what remains after one has forgotten what one has learned in school." - Albert Einstein
2
 
Hey, everybody!
 
7:21 PM
@Khallil wave
 
hi pal
 
That quote is one of my favourites, @IceBoy!
Two armed wave, @Hippa. ^_^
I finally cleaned my room! =D
 
ヽ(・ω・)ノ
@Khallil better ?
 
\(^∀^)メ(^∀^)ノ
 
ლ,ᔑ•ﺪ͟͠•ᔐ.ლლ,ᔑ•ﺪ͟͠•ᔐ.ლლ,ᔑ•ﺪ͟͠•ᔐ.ლ
(づ。◕‿‿◕。)づ(づ。◕‿‿◕。)づ(づ。◕‿‿◕。)づ(づ。◕‿‿◕。)づ
 
7:25 PM
I bow to your mastery of the emoticons, @Hippa! ^‿^
 
٩(⁎❛ᴗ❛⁎)۶
(removed)
:P
 
@Hippalectryon Something fell down on my keyboard ... :-)
 
Uh
Blame Newton
 
Actually it's the book I wanna show you ...
 
:O
SHOOWWWWWW MEEEEEEEEEEE
Show me or else
 
7:36 PM
:-O
 
This is the first English book I had, and it has an interesting story. My mom took it from someone that wanted to throw it and she brought it home. A month later I knew to read and write in English.
 
Uh
It took me some years
 
Here is another picture with a lesson inside.
(I can't upload anymore)
 
?
Why ?
because sharks
 
@Hippalectryon Failed to upload image, please try again!
 
7:44 PM
:/
 
So. I know that $z(x)=a_1(x)g(x) mod(x^n-1); g(x)=b_1(x)*z(x) mod(x^n-1); x^n-1=q_1(x)g(x)$
 
Wait, I have a solution for this ...
 
I want to show that $gcd(x^n-1, z(x))=g(x)$. Suggestions on path to solution?
 
@Hippalectryon
 
@Chris you are spanish? Or portugese?
 
7:47 PM
@Studentmath Romanian
 
@Chris'ssis Uh shall s everywhere
 
One does not simply shallinate
 
@Hippalectryon Yeap.
 
@Chris'ssis that's Romanian? Wouldn't have guessed.
 
@Studentmath Yeah. :-)
 
7:49 PM
Well they could have used even weirder words
 
:-)
 
Like begat, whereinsoever, ...
 
So I am thinking, assuming $f(x)=u(x)g(x)+r(x)$ and then assume it divides both $z(x)$ and $x^n-1$, and get a contradiction. However I don't manage to get a contradiction..
Which is very depressing.
If I could show $r(x)=0$ for sure it would be enough.. I do have that $g(x)$ must divide some $a_2(x)r(x)$ and $q_2(x)r(x)$, but that doesn't tell me $g(x)$ divides $r(x)$.
Just tells me it's more likely to..
 
@Hippalectryon That's a clear jumble-up of two gifs.
 
Like whales better ?
 
7:57 PM
lol
 
I still prefer fruit ninja though
 
@Hippalectryon That's not a humano-whale. There is an underwater volcano inside the lake, which bursted just when the man entered the water.
 
whoa
hahaha
 
If you want I can also learn you to fish
 
8:00 PM
HAHAHA
@Hippalectryon Pity capital letters are fixed under capitalisation.
 
:c
What about horse jumping ?
 
Yeah that will give me nightmares.
 
wonders if @hippa has no work except to collect funny gifs
 
This was a good time to visit the chatroom
 
@BalarkaSen Physics
And war
 
8:03 PM
She looks like that girl from that horror movie.
Exorcist?
 
@Studentmath Ask the parrot
 
Gah, this question was way simpler than I thought.
 
The parrot would have told you so
 
@Alizter want a reveal of the problem?
 
@Hippalectryon That fruit ninja one is quite funny.
 
8:12 PM
I have a last 'funny' image but it's about 9/11 :c
So i guess I won't post it
 
you have to post it
it's 9/11 anniversary
 
:c
Urm i don't wanna shock people
do I ?
 
I don't even see how it's such a big deal? Humans use violence to get what they want, what's new?
How is 9/11 any worse than the notion that parents must punish their children for acting wrong?
 
Ok - beware below, it's just for fun, nothing serious
 
lol screenshot-ception
A screenshot of an anonymous communication website showing a screenshot of an anonymous communication website
 
8:20 PM
Still, I can't believed i laughed that much at this one
Here a last one for today
 
8:55 PM
Compute elementarily
$$\lim_{n\to\infty} \frac{\displaystyle 3^{3n} \binom{2n}{n}^2}{\displaystyle \binom{3n}{n} \binom{6n}{3n}}$$
no integration
 
no Stirling's formula
 
I was about to try Gamma -> Beta
 
@Hippalectryon Do it by the squeeze theorem.
 
What is that ?
Upper bound - lower bound with same limit ?
 
8:57 PM
In calculus, the squeeze theorem (known also as the pinching theorem, the sandwich theorem, the sandwich rule and sometimes the squeeze lemma) is a theorem regarding the limit of a function. The squeeze theorem is a technical result that is very important in proofs in calculus and mathematical analysis. It is typically used to confirm the limit of a function via comparison with two other functions whose limits are known or easily computed. It was first used geometrically by the mathematicians Archimedes and Eudoxus in an effort to compute π, and was formulated in modern terms by Gauss. In Italy...
 
hi guys I need a hint with one exercise in dudley´s book: Define a complete metric for R\{0, 1} with usual (relative) topology. So we hae to define some metric with generate the same topology that the usual one in R\{0, 1} but makes this last one complete...
Someonce could give me a hint?
please
 
No, we don't serve strings here. Get out.
joking
 

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