Mathematics - 2013-04-01 (page 4 of 5)

@JohnCarpenter OK, just multiply the whole series by $x$.

@DominicMichaelis why is that hilarious ?

9:18 PM

cause it obvious fails there

@JohnCarpenter OK, maybe what I'm giving you is not totally legitimate.

...

and 2 is hilarious cause it is such a large number one would never try to test for a conjecture

Up to $(0,4)$ we're good.

Hey @MattN. long time no see

You can use a $\log$ alternating series if you want to @JohnCarpenter

9:20 PM

darn - I scared him away again :(

John Carpenter

Ok I'll figure it out

thanks guys

@CтарыйДжон I think I did

@John i would chose $$\sum_{n=1} \frac{1 }{n} \frac{(x-2)^n}{2^n}$$

I'll take the blame.

@PeterTamaroff maybe both of us - we clearly are pretty scary in total

9:21 PM

@DominicMichaelis Wait...

oh wait we don't need the -1^n

@DominicMichaelis Precisely.

@DominicMichaelis Good job.

Hi all.

@CтарыйДжон ???

@t.b. Yay!

9:23 PM

@mick sorry - what are you asking?

@CтарыйДжон why do you scare ppl away ???

What's up?

@t.b. I am trying to prove that every additive subgroup of $\Bbb R$ is either discrete $\alpha \Bbb Z$ or dense

Jonas Teuwen

@tb Hi.

What the heck.

tb?

9:25 PM

@mick i gave you a table of values you obviously see that your conjecture is pretty wrong+

@mick because I am old and eat small furry animals

4

@t.b. It is based on whether $\inf G^{+}>0$ (discrete) or $\inf G^{+}=0$ (dense) where $G ^{+}=\{g\in G:g>0\}$

Yeah, why the hell is that making it t.b.?

@DominicMichaelis where ??

@CтарыйДжон HAHAHAHAHAHAHA LOL

@PeterTamaroff :)

9:27 PM

$$\left(
\begin{array}{ccc}
2. & 2 & 2. \\
16.6774 & 2.69315 & 22.2226 \\
38.5346 & 3.68386 & 49.6249 \\
61.8528 & 4.98782 & 78.4884 \\
86.2607 & 6.59482 & 108.441 \\
111.645 & 8.4811 & 139.371 \\
137.945 & 10.6189 & 171.217 \\
165.125 & 12.9816 & 203.941 \\
193.155 & 15.5451 & 237.516 \\
222.016 & 18.2889 & 271.923 \\
251.692 & 21.1951 & 307.144 \\
\end{array}
\right)$$

Ok, fun's over. But gotcha. :P

@MattN. how are things?

left is the left hand side

in the middle the midle

and on the right the right hand side

g[n_] := Sum[N[Nest[ArcSinh, n/2, m]], {m, 1, 100}]
f[0] = 2;
f[n_] := N[ f[n - 1] + Log[f[n - 1]]]

@DominicMichaelis Well, what if we reopened and you put that as an answer?

Table[{2 + Log[2] (g[n] - 4)*n , f[n], 2 + n* (g[n] + 4) Log[2]}, {n,
0, 10}] // TableForm

9:28 PM

im gonna look at my excel file

@CтарыйДжон Good. And yourself? Sorry, was afk making some coffee.

@MattN. OK here, thanks - just plodding on ... with maths and guitar and a couple of languages ...

@Peter i don't know I can do that if you like

I'll be back shortly. The "fooling" didn't last very long it seems.

darn - I must remain silent - people are starring too much of what I say!

6

9:32 PM

What languages are you up to these days?

@MattN. Mostly Russian and Persian, with a bit of Arabic

@CтарыйДжон Reminds me: I found out why I used to think Na zdrowje was cheers in Russian: it is cheers in Polish. And I have all slavic language stored on the same neuron...

Is there someone on here who wouldn't mind helping me with tensor multiplication?

@MattN. Russian has a couple of expressions which sound almost the same

Need to learn one slavic language to be able to hear and tell the differences.

9:35 PM

@Nick @Expert should do the job.

"na vashe zdorovie" = "to your health" (I think)

@CтарыйДжон I want to learn Russian so badly! But they say it is friggin hard.

Expert

@Nick what's up?

@mick oh i forgot to devide by 2 then only the lower bound is wrong

@CтарыйДжон I tried to prove something and failed. Then I got depressed.

9:36 PM

Wait, so the expert isn't a bot? Crap, I had a strange conversation earlier then...

@PeterTamaroff Not as hard as Mandarin - I gave up on that after a year :)

Do you guys agree using $\sum_{k=n+1}^\infty$ is just obscuring notation?

@CтарыйДжон Hehehehhee.

@CтарыйДжон Yes, like "santé" in French the Polish one can be used to say either as cheers or as bless you when you sneeze.

@Nick this expert is anon

my values seem correct.

9:37 PM

what are your values ?

@DominicMichaelis I thought about saying it and then decided that it would spoil the fool's joke...

@Nick I assure you it will successfully solve your problems. Money back guaranteed!

@Expert, so I have an expression $\vec{\nabla}\cdot(\rho \vec{u} \vec{u}$

@mick Why do you even care about that big ass recursion? Is it of any value?

Hmm.

9:38 PM

@MattN. i don't like april fools anyway :)

Expert

oh, those tensors. well, okay then.

@PeterTamaroff the value is understanding recursion better of course !

@DominicMichaelis I don't particularly like any type of fools :)

4

This will be starred shortly...

4

(not by me)

indeed

9:39 PM

: )

(by me)

:p

Let me retry that: ∇ *(puu)

@mick how to hell you make it with excel and since when excel does have an option for infinite sums ?

Where ∇ and u are vectors, p is a scalar, and * is the dot product

@MattN. I have Segafredo black coffee. Yum!

9:40 PM

So, I guess direct multiplication of two vectors (length 3) results in a 3x3 matrix.

But then what does it mean to do a dot product with a matrix?

I thought dot product was only defined between two vectors.

@MattN. This one

@PeterTamaroff I have never heard of it. Is it good? The other day I thought I will (in the near future) put some effort into learning how to improve my coffee skill.

@MattN. It is good, yes.

@PeterTamaroff But this one looks as if you're buying it ground...?

@DominicMichaelis the taylor series of arcsinh(x/2) is x/2 + O(x^3) so the infinite sum converges very fast ( about exponentially : 2^n )

9:42 PM

@matt took me some years to discover the knack of creating a decent espresso

@MattN. Yeah. It comes ground, but void sealed.

@Expert, are you there?

Expert

@Nick the divergence operator is $\partial/\partial x_1+\cdots+\partial/\partial x_n$, you can apply that to a matrix

April Fool's Day has turned into $\Huge\text{Star CтарыйДжон Messages Day!}$

wait wait wait you take a taylor series for a recursion? do you know how those errors are enlarged ?

9:43 PM

@PeterTamaroff But then it's already lost most of its taste : ) My first step towards making better coffee was to buy a decent grinder.

@κρανίοπεριπολία when you read that aloud it sounds like you have a stutter!

but neverhte less

@MattN. Hmmm, well. If I could, I would spend all my money in a super deluxe coffee machine and a barista to make it!

what values do you get ?

@DominicMichaelis iterating x/2 + O(x^3) near x = 0 grows approximately like C x/(2^n) for some real value C.

9:44 PM

at least for f i think excel wit hthat

@PeterTamaroff Like Jonas? : )

@MattN. Jonas has a barista?

=)

@PeterTamaroff No, I mean he is a barista.

afterall x= 0 is the fixpoint of arcsinh(x/2)

@Expert, thanks

9:44 PM

Sort of.

He's a coffee geek, I think.

2

ok give me a list of your f values

@MattN. All hail @JonasTeuwen

4

can I unstar ?

would you give me your f values now ?

@mick yip within 30 sec

9:47 PM

or shall i tell mine first ?

What a bad day. I will go now. Be seein you!

@MattN. What happened?

@DominicMichaelis how about n >2 do you agree on the conjecture then ?

Thomas

How can one disagree with a flag in the review section? I see a button for "flag or disagree", but I can't figure out how to indicate tha I disagree

@DominicMichaelis you do realise g(n) is like ln(n) + ln(ln(n)) + .... ?

9:50 PM

no

Henning Makholm

@Thomas Flag it as "invalid flag".

@MattN. why ?

Thomas

@HenningMakholm: Thanks!

g(n) is like (arcsinh(n/2))+ arcsin( arcsin(n/2)/2) + ...

the left hand side grows faster then linear

@DominicMichaelis which is asymptotic to ln(n) + ln(ln(n)) + ... where we take as many logs until we reach about 1.

9:52 PM

@mick yeah but you multiply with n so you have faster than linear

archsinh , not arcsin

i know just forgot the h

@DominicMichaelis do you think that matters alot ?

$$\left(
\begin{array}{ccc}
2. & 2 & 2. \\
-0.0834504 & 2.69315 & 5.46173 \\
-0.831843 & 3.68386 & 10.2585 \\
-0.347123 & 4.98782 & 16.2884 \\
1.2592 & 6.59482 & 23.4399 \\
3.89408 & 8.4811 & 31.62 \\
7.48794 & 10.6189 & 40.759 \\
11.9905 & 12.9816 & 50.8067 \\
17.3651 & 15.5451 & 61.7265 \\
23.5848 & 18.2889 & 73.4914 \\
30.6291 & 21.1951 & 86.0808 \\
\end{array}
\right) $$

yeah i think that matters a lot as you see

@mick you don't appreciate getting help or ?

$10^{2010}-1=9N$ as N = $1111...11$ (1 is repeated 2010 times)
how can I prove that

9:56 PM

its trivial @pourjour

@DominicMichaelis but N

10^2010-1= 999... 999 with 2010 times a 9

so you are saying (arcsinh(n/2))+ arcsin( arcsin(n/2)/2) + ... - ln(n) + ln(ln(n)) + ... > 4 ? or < 4 ( if i switched sign wrongly )
@DominicMichaelis

@DominicMichaelis and how could I've notice that?!

@pourjour well 10^2-1=100-1=99, 10^3-1=1000-1=999 don't you see a system ?

user19161

10:00 PM

@DominicMichaelis Huhu. I am now the blue square.

@JasperLoy blue looks neater at you :)

user19161

@DominicMichaelis I just saw the Gmail Blue ad, I am not sure if it is going to be rolled out soon.

@DominicMichaelis yeah so I could use induction to prove it

@κρανίοπεριπολία arg: I just realize you asked me this morning whether I've found anything regarding 5pm. No... still nothing. As I've been suggested, I flagged a random post, and asked the question hoping for a moderator to get back to me

@pourjour use that 9+1=10 ^^

10:02 PM

@DominicMichaelis hmm I couldn't find a formula

@mick you missed a times n on the arcsinh part

@pourjour not that 100= 90 + 10 = 90 + 9 +1

note *

@WhitAngl It's probably best to ask a Math moderator.

essentially the same (because then we get ) :
n ((arcsinh(n/2))+ arcsin( arcsin(n/2)/2) + ...) - n (ln(n) + ln(ln(n)) + ...) > 4n ??

@DominicMichaelis I will take a walk and back again, this is a headache :(

nope you don't have a times n part in the log term,

do you even know which inequality you want to prove ?

10:05 PM

@κρανίοπεριπολία apparently, flagging random posts is the best way to contact moderators ;)

i give you 5 minutes to tell me your values for your left hand side from n = 1 to 10

@DominicMichaelis But i do , read

that shouldn't be a problem if you already have an excel table

mmm... unless that was an april fool's joke ;)

@WhitAngl No - I think Henning was being serious

10:06 PM

ok :) that's what I did anyway :)

@DominicMichaelis I tried to approximate ln(n) + ln(ln(n)) + ... with arcsinh(n/2) + arsinh(arcsinh(n/2)/2) + ... Isnt the difference a small constant ?

a small constant times n gives big trouble for great n

@DominicMichaelis yes but that is where the 4 comes in.

as my table shows 4 is not a good constant for that

@κρανίοπεριπολία Skullpatrol?

10:10 PM

by the way the 5 minutes are over

i am tired and you still didn't gave me a single value you computed

@Charlie Yes.

@DominicMichaelis do you agree for n >10 ?

@DominicMichaelis maybe i need to reconsider my values ...

@κρανίοπεριπολία I lost my connection :'(

i don't even know what your values are everyone can make mistakes ...

@Charlie Ok :-)

10:12 PM

@DominicMichaelis oK but its in a few files just a sec

@κρανίοπεριπολία :)

@Charlie :)

user19161

Hi @WhitAngl why are you so interested in 5 pm?

you really strethc my patience @mick

@κρανίοπεριπολία you logged off.....i thought you gave up on me....

10:15 PM

@JasperLoy I think the correct spelling is "5pm" (no space) :))))

I will give a table of true value minus (ln(n)+ln(ln(n)+...) @DominicMichaelis

user19161

@CтарыйДжон LOL.

@JasperLoy I am training to be a GN too :)

@Charlie Nah, I went afk.

user19161

@CтарыйДжон I see. I will award you your cert soon. =)

10:16 PM

@JasperLoy Thank you, master! :)

user19161

So is Gmail Blue an April Fool thing?

@κρανίοπεριπολία aah :)

how do i paste from excel ? @DominicMichaelis

i don't know i never use excel

user19161

@mick You simply paste.

10:20 PM

0,521499357
0,338224507
0,270935451
0,260612449
0,28065775
0,31738575
0,363241633
0,413870364
0,466689662
0,520141983
0,573281562
0,62553717
0,676571364
0,726194715
0,774312359
0,820890059
0,865932328
0,90946814
0,951541522
0,992205312
1,031517019
1,069536068
1,106321992
1,141933255
1,176426511
1,209856152
1,242274064
1,273729514
1,304269132
1,333936948
1,362774477
1,390820822
1,418112787
1,44468501
0,194224821
0,211836666
0,229079345
0,245964437
0,262503279
0,278706925
0,294586117
0,31015127
0,325412458

user19161

@expert You look pretty today, lol.

there they are

@JasperLoy you look pretty today, jasper

always between -4 and 4 as conjectured

user19161

@Charlie I am always pretty.

10:22 PM

@Charlie Do I look pretty ?

@JasperLoy you are the king banana

user19161

@κρανίοπεριπολία Haha.

@mick I don't know

Just say yes @Charlie

user19161

I have no idea why so many people think I am gay. I am straight.

10:23 PM

the lhs is negative for low n

your result can't be true

I'm not fond of.yellow

@JasperLoy I would like to acknowledge 5pm for one of his answers in a paper, and would like to get in touch with him, so as to put his real name rather than a pseudonym that doesn't even exist anymore

@DominicMichaelis I took the difference add sign

@Charlie *yellow

user19161

I think "blue" is my favourite colour for now. I have just changed my desktop to blue and gmail to blue as well.

user19161

10:24 PM

@WhitAngl I see. I am afraid he wants to remain anonymous.

@mick $\huge \text {NO.}$

Ill give another table ; 2 , 2 + ln(2) , ... @DominicMichaelis

user19161

In fact, Alexander Grothendieck could be on this site, disguised as a banana.

@κρανίοπεριπολία ;)

2
2,693147181
3,683857646
4,987818122
6,594816686
8,481100676
10,61894091
12,9815802
15,54511164
18,28885787
21,19514989
24,24892226
27,43729444
30,74919763
34,17506153
37,70655772
41,33639174
45,05813501
48,86608856
52,75517223
56,72083404
60,75897563
64,86589045
69,03821236
73,27287252
77,56706297
81,91820586
86,32392712
90,78203394
95,29049534
99,84742541
104,4510687
109,0997874
113,7920503
118,526423
123,3015589
128,116192
132,9691296
137,8592466
142,7854798
147,7468231
152,7423233
157,7710756

10:25 PM

@Charlie };)

user19161

@mick I see you use comma for decimals.

@JasperLoy Its peanut butter gelly time !

@JasperLoy oh ok, thanks :s did you ask him ?

@JasperLoy yes but this comes from excel !

user19161

@WhitAngl No, but someone who doesn't want to use his real name probably wants to conceal himself. I don't know 5pm by the way.

10:27 PM

@κρανίοπεριπολία O;)

@DominicMichaelis I sent another list above

user19161

@mick There should be no space before !

my internet doesn't work

$$\left(
\begin{array}{ccc}
2. & 2 & 2. \\
-0.0834504 & 2.69315 & 5.46173 \\
-0.831843 & 3.68386 & 10.2585 \\
-0.347123 & 4.98782 & 16.2884 \\
1.2592 & 6.59482 & 23.4399 \\
3.89408 & 8.4811 & 31.62 \\
7.48794 & 10.6189 & 40.759 \\
11.9905 & 12.9816 & 50.8067 \\
17.3651 & 15.5451 & 61.7265 \\
23.5848 & 18.2889 & 73.4914 \\
30.6291 & 21.1951 & 86.0808 \\
\end{array}
\right)$$

user19161

@WhitAngl There should be no space before ?

@JasperLoy I like it !

user19161

10:27 PM

@mick -1.

user19161

This is an English exam!