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15:02
Earlier you said "Some people think "n" is not a number.
but then how can n = 3?" would you care to elaborate on that sir?
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how?
2 is not a number, to the arabs, or the chinese.
@QED What did you mean?
@QED Was this a statement about the use of "n" for a variable?
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I've talked to people before who think there's something special about numerals
like 35 is in some way different than m or n
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15:05
but it's not
35 and m and n are just symbols, which we give meaning...
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yes
Qed I sort of hate you now
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why
Giving me too much to think about, before my exam tommorow..
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15:07
don't worry so much about exams
If we asume 2 and 3 are just symbols, which we say represent the quantity of two and three oranges.
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I tried supposing that x is of the form $\frac{A + \sqrt{B}}{C}$ and computing the RHS of $x = (x^2 - a)^2 - a$.
but the expression you get in the end is pretty complicated.
@QED As explained in the link the definition of a variable is circular
That is my defininiton of 2 and 3. 2 represent the quantity of two oranges.
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(we want to solve A,B,C in terms of a)
15:08
Now how would i represent some irragular number?
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@Skullpatrol, maybe that definition sucks? I use lambda calculus instead
@N3buchadnezzar oranges are irrelevant
and misleading
Well symbols needs to have a definition =)
@N3buchadnezzar With a variable it is a symbol used to represent one or more numbers
Thats a circular definition
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15:13
What am I saying is that n is a number
n is a letter, last time I checked sir
@QED A rose is a rose is a rose
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I think you need to learn lambda calculus to understand the point of view I am suggesting
I said you need to learn it
My apologies
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it's a very worthwhile theory to learn
OK, I'll give it a try.
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15:25
The best text I know of is this you only need chapter 1
WOW!!! thanks that's a great resource
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yeah :)
Before I go diving into the book could I tell you what an old teacher of mine used to say about "Some people think "n" is not a number.
but then how can n = 3?"
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yes
n = 3 is an equation that is true when only 3 is substituted for n
3 = 3 is a true statement
@QED How does that sound?
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15:35
that's fine
@QED Thanks again for the great reference ... bye
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bye
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this reminds me of a great picture I once saw on the internet
@Asaf: are you here?
@QED Quod Erat Demonstrandum
15:38
Someone solved a second order differential equation, using his own symbols. Like dogs, rats. Rather funny.
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heh
@Ilya, How you doing?
@Srivatsan hi ) well, I'm almost ok. how about you?
I'm good. In which part of the world are you in right now? Netherlands?
15:43
in Old one )
I have a lame question in elementary set theory, would you help?
very lame
Sure, go ahead.
ok, there are two sets: $A$ and $B$
let $A'\subset A$ and $B'\subset B$
@Srivatsan I've a Q in probability ,can you help pleaseee?
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I wish you would say question instead of Q.
15:47
@FreakEnum Wait for a little bit. Middle of something, as you can perhaps see... =)
There are 6 girls and 6 boys , what is the probability so that no girl sits together?
I don't need solution but why my method is wrong I want to know
hell. let me think...
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@FreakEnum I think that question isn't specified well enough
you need to say more to define it
@AsafKaragila Ilya has a lame question in elementary set theory, would you help?
if I can construct two injective maps $f:A'\to B$ and $g:B'\to A$ does it mean that $|A| = |B|$?
15:51
@QED there are 12 seats total on which 6 G and 6 B are to be seated .
@FreakEnum round table?
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It's still not enough
@Ilya no
@Ilya If that's all the requirements, then no, right? Take $A'$ and $B'$ to be singletons...
@Srivatsan yeah, that's why it was delay and hell
@QED smth bothers you, doesn't it?
15:53
@Skullpatrol Are you trying to irritate him (or for that matter someone else here)? =)
@Ilya My A would be Y. =)
@Srivatsan Not really
@QED 6 boys and 6 girls sit in a row at random. Find the probability that the boys and girls sit alternatively
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@Ilya, yes
@FreakEnum, you can just count the ways they can sit alternatively (2) and then the total number of possible ways to sit
@Srivatsan: thanks
@Ilya For listening patiently? :=)
You're welcome, of course.
15:56
ok , letme post my solution so that you guyz can help me what I did wrong
@FreakEnum OK. First, I will state the question clearly for reference. There are 6 boys and 6 girls, they are made to sit in a line in a random order. What's the probability no two girls end up next to each other?
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@FreakEnum had you already solved it before asking here?
@QED yes
@Srivatsan yes
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You shouldn't do that :/
@QED - why not?
I can't tell if you're joking or serious.
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15:58
you should say you need to check your answer
rather than asking how to solve something
- which FreakEnum did, somewhere in between...
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?
my solution :
Sample space = 12!;
now, Lets 6 boys sits first on 6 chairs , then no of ways = 6!;
now girls can be sit on 7 places i.e Boy= "*" , Girl="#" , Seat = "_" , so _*_*_*_*_*_*_
so girls can be sit in = 7P6 ways;

so my answer (6! * (7P3))/ 12!
wait. This looks reasonable, but I somehow doubt every step of this...
What's 7P3 doing here?
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16:02
I'm happy to help people if they're stuck with something I can do, but I think it's unhealthy to get into the habit of checking answers
@Srivatsan sorry , typing mistake = answer = so my answer (6! * (7P6))/ 12!
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also if you're in school you should let the teacher check your answers instead of people online
All the possible combinations of placing 6 persons on 12 chairs, $minus$ the possibility that they are evenly spaced
@N3buchadnezzar Almost, but not that simple.
@QED no I don't want to get answers to be checked but need help to know what I did wrong. Sorry if that hit in bad way
16:04
I figured =)
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it's fine, I'm just explaining myself
@N3buchadnezzar What about #**# *#*#*#*#?
* = boy and #=girl, space is only for readability.
Why not simply label them B and G...
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There are 12! ways 12 people can sit in a row
@N3buchadnezzar I did that before I posted. It wasn't easy to read a string of 12 letters clearly.
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16:07
There are 2 * 6! * 6! ways they can site alternating gender
@FreakEnum I don't know what's wrong with this. But can we try with 2 boys and 2 girls?
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@DylanMoreland, you've not met VVVVVVVVVV then.
@DylanMoreland Actually, this is the not the first user with such a name. There was a someone with a handle like "qqqqq*qq*qqqqqqq" (The *'s were actually two other letters. I don't remember the exact handle, obviously.)
@Srivatsan sure :)
16:12
@FreakEnum Forget dividing by 4!. Let's calculate the number of ways. Your answer is 2! x 3P2 = 2! x 3! = 12.
@Srivatsan yes
Let's say A and B are girls, X and Y are boys.
3 | 2 | 1| 3 | 3 , which adds to 12.
I don't know, seems to be right. =)
Your logic also seems right actually.
Why do you think there's a mistake?
@Srivatsan because my answer mismatches book's answer :(
16:20
@FreakEnum What is the textbook answer?
for our 2 b and 2g's , it's 2* 2!*2!
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You should just ignore the text book answer
solve the problem in such a way that you know you've got it right
@QED How do we know we got it right?
@FreakEnum Can you state it for a general $n$ boys and $n$ girls?
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write the answer out clearly using small logical steps
voila , I got what's wrong :)
16:22
@FreakEnum What is? =)
@Srivatsan They must sit alternatively, but in my solution I'm also including this one GBBG also
@FreakEnum Of course, that's allowed. You only said the girls should not sit together. Why should they sit alternatively?
@Srivatsan in Q they must sit alternatively
@FreakEnum And you stated a wrong question to us, then... =/
@Srivatsan I really apologize for that , please forgive me :(
16:27
@FreakEnum No problem. Just be more careful in the future -- for your own sake, more than anything else.
Thanks to all of you who always help me anytime :)
@QED sorry for pestering you too :(
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you didn't pester me at all
I don't think you agree with my ideals though
which are that you should try to forget about checking answers and looking up things in the back of the book
I think it's best to solve problems in such a way that you know you've got it right
but I guess people don't like that because you don't have a safety net (although that's sort of the point) and it's harder
True!, Thank you all again :)
@QED For what it's worth, I disagree with this viewpoint. Actually, it does make a lot of sense, provided it works. However, there are many situations where you see things only hazily -- where one is forced to guess, to stumble, to err. It may not happen for such textbook problems, but I think it's inevitable when you start doing more and more nontrivial ones, let alone in research.
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I have no experience with anything like that
To be honest I don't really believe that math research is possible seeing how many centuries people have been working on it (but I'm obviously wrong because people are doing it all the time)
16:38
@QED I don't understand. When you say "people are working on it", what is "it"?
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post graduates doing new math research
I would have thought all the stuff you could possibly do at that level would have been done already
It seems like the only way I could get to new mathematics is after at least a decade of work
of course the evidence is contradicting this but I don't understand what's going on
@QED Can't say too much on that. =)
[Not experienced and all that...]
@Ilya, there?
There was a lst posted on the site, with the greatest mathematical discoveries during the last year.
I found that list interesting.
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can you link it please?
And it seems more and more concepts and ideals are developed in math, deeper and deeper abstract concepts.
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16:52
I didn't see this
It seems like math has moved on from being a practical tool for phycics into a realmn of its own.
@N3buchadnezzar It seems? Oh, that one's a modest thing to say.
So I see math as "discovering beautiful relations and beautiful things"
The analytic mathematicians tends to disagree on that one...
@N3buchadnezzar "analytic" mathematicians?
I am not sure.
Numerical mathematicians? blaims bad english
16:55
Out of curiosity, did you ask any of them and they disagreed?
If you don't mind, I think I will stay away from more of this discussion.
I just happen to like talking mathematics more than talking about it.
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Do you know any complex dynamics?
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thanks N3buchadnezzar
I think that will be a good read
I guess I stopped studying complex analysis because I thought I probably wouldn't be able to learn the complex dynamics
I should just continue
17:11
A timeline of pure and applied mathematics history. Before 1000 BC * ca. 70,000 BC — South Africa, ochre rocks adorned with scratched geometric patterns. * ca. 35,000 BC to 20,000 BC — Africa and France, earliest known prehistoric attempts to quantify time. * c. 20,000 BC — Nile Valley, Ishango Bone: possibly the earliest reference to prime numbers and Egyptian multiplication. * c. 3400 BC — Mesopotamia, the Sumerians invent the first numeral system, and a system of weights and measures. * c. 3100 BC — Egypt, earliest known decimal system allows indefinite counting by way of introducing n...
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"Tomas Rokicki, Herbert Kociemba, Morley Davidson, and John Dethridge proved that diameter of the Rubik's cube group is 20."
I'm not sure how this is a significant result
Is there anything to that, other than having a powerful enough computer?
group theory?
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17:27
Since it's not that fun when you don't know the rigor behind it
@QED I don't get you
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What is it?
@QED I didn't understand your previous comment. Are you saying that group theory is not fun?
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I was still talking about complex analysis
Oh =)
17:37
hi folks
This is the first dinner I have made
that I am not able to eat
@N3buchadnezzar How did it come to to be?
Why not?
it tastes soo bad..
Tried to hide the hhorrible taste by using hot spices and spices in generall
You're the first person I've heard who didn't like their own cooking =)
Only made it worse...
Dinner was all the remaining food in the fridge
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17:43
I don't really know much group theory at all
I liked that composition series
since it gaves another proof of the FTA
unique factorization
Jordan–Hölder theorem
That's probably the deepest group theory I know..
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18:00
:/
18:12
@Ilya I'm here now...
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18:24
Why are you trying to be mean
QED: Well, what's your explanation for what Skullpatrol was trying to do?
Are you both asking me?
@AsafKaragila No, I was asking QED. I didn't like what S. did either. E.g., see chat.stackexchange.com/transcript/message/2760799#2760799.
Anybody know the natural density of squarefree numbers congruent to a modulo b?
18:44
@anon Did you try to make a probabilistic calculation?
I did last night but I don't remember what I did.
(I'm working on a q-problem over on mse..)
Hello, everyone!
hi Daniil
18:47
gah, I absolutely loath time constraints on doing math
Hey, btw, what happened to your job? I don't think we've met for some time...
The friend who hooked me up has disappeared off the face of the Earth, kicked out by his wife, and the place said they have no idea who he is. And he took some of my shit, which really pisses me off.
@anon Oh, I'm sorry to hear that.
19:16
Hmm, well, if you sum $n^{-s}$ over squarefree integers equal to $a\mod b$ you get $$\sum_{\chi\mod b}\frac{\overline{\chi}(a)}{\varphi(b)}\frac{L(s,\chi)}{L(2s,\chi)},$$ that's something at least.
Sorry, I don't follow this subject...
Do you know what a Dirichlet character or L-function is?
No. =) // I corrected my previous comment.
Well, that's what you'd need to know. :)
But if I must make a guess, I would do the following. For simplicity, let's first assume $b$ is a prime number, and $a$ is nonzero modulo $b$. Then $n = a \pmod b$ is square free if for every prime $p \neq b$, $p^2$ does not divide $n$. There is no condition imposed by $b$. So this gives the probability
$$
\prod_{p, p \ne b} \left( 1 - \frac{1}{p^2} \right) = \frac{6}{\pi^2} \cdot \frac{b^2}{b^2-1}.
$$
19:25
He's back, and he's got arak with him! Watch out!
anon: Does this make any sense?
@AsafKaragila Is this the boogeyman?
@Srivatsan He cannot boogie, man.
Bah, that's annoyingly straightforward. I presumed a would come into play somehow but it doesn't, really.
Anyway, I have to go now. Later.
@anon Um, does that mean that you believe what I just said? =)
Dependence on $a$ does come up: for instance, when $a$ is zero mod $b$, then this expression now changes...
I presume that this gets multiplied by $\left( 1 - \frac{1}{b} \right) = \frac{b-1}{b}$, instead of $\left( 1 - \frac{1}{b^2} \right)$.
All this get more complicated if $b$ is a composite number...
20:18
Back from the doctor. Well, I stopped off to answer a question first $\stackrel{\circ\ \circ}{\smile}$
reading backlog
Hey robjohn, plus one for the complex analysis thing that you just answered. I wonder why Byron deleted their answer.
Can I ask you guys here in the "pub" a question about uniform convergence?
@robjohn, can you explain to me what the following excerpt is trying to say:
Hardy's "Course..." I'd need to investigate years-of-publication and such, but I know the provenance of that thing needlessly well. My father (a high school math teacher in the U.S. required to obtain a higher degree [sic] in mathematics) endured a night-school course whose text was Hardy's. I was not very old, but old enough to be ... stunned... by the tendentiousness of that text. I had a fair understanding of analysis in the late 1960s, and/but Hardy's text effectively expressed doubt that its reader "had a brai
I am especially stuck at the word "tendentiousness". Dictionary search says something like "having a tendency", "biased". But that doesn't make much sense to me in this context...
This para is from this answer.
@Srivatsan Sorry, I accidentally closed the chat window. Let me read...
Whoah, tomorrow I've got an appointment to discuss a mortgage!
20:33
I wonder why people write answers that make me browse through dictionaries... =/
@JonasTeuwen sign on the dotted line, and all your problems will disappear...
@JonasTeuwen Mortgage? What's that about?
@Srivatsan I have to, as well, so don't feel too bad.
@robjohn Or I will get new ones for the coming 30 years? 8-).
@Srivatsan A house! Well, apartment.
@JonasTeuwen I was recalling what Rumpelstiltskin said in Shrek 4
20:34
@JonasTeuwen I don't get it. You are mortgaging a house? Or renting it?
@Srivatsan No, I want to buy one.
@JonasTeuwen Oh, that's nice.
And I don't have 120k lying around.
@robjohn So, she wasn't actually honest when she asked me to sign on the dotted line!? ;)
@JonasTeuwen Good luck anyway.
Thanks 8-).
@robjohn Oh, I should see that movie.
20:39
You know what, I think that word was thrown around just like that. Perhaps p.g. assumed no one would be jobless enough to check a dictionary... =)
@Srivatsan I don't exactly know what he is trying to say in that passage. Provenance means origin; he knows the origin or source of the book?
@robjohn did he mention the word provenance?
And what bias is he referring to with tendentiousness?
I assumed he meant to say the bias towards making the reader feel like a brainless idiot.
@robjohn was ... stunned ... by the «attention to detail or thoroughness» of the book. makes sense. But tendentiousness?
20:46
I'm stuck on problem , May I ask the Q?
Sure.
From now on I would like you guys to address me as: "Dear Leader, who is a perfect incarnation of the appearance that a leader should have". Thanks in advance!
Now what triggered that?
@Srivatsan This guy is disappointed with the lack of exercises in the book, and he is ranting about everything he can, it seems.
20:48
Q: There were 32 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by $42 per day while the average expenditure per head diminished by $1. What was the original expenditure of the mess?
@robjohn Yes, that's the overall context. But this para -- which put me off quite a bit on first reading -- is a bit off, it seems. Agree?
Sorry for putting you through this, @robjohn =)
@Srivatsan It may be that either we are incapable of understanding, or he is using words beyond his paygrade.
@robjohn Hey, no way we are conceding the first possibility. So... :)
@Srivatsan $\stackrel{\circ\ \circ}{\smile}$
@JonasTeuwen I am quite amused at how you are an incarnation of an appearance. =)
20:51
:(.
@FreakEnum You should perhaps show some work. (Nod to what QED said a few hours back.)
@Srivatsan I've no idea this time how do I solve this :(
Q is bit twisted , that's why want to learn the steps or procedure
@FreakEnum First introduce a variable for what you want to compute:
Let E denote the expense for $32$ people per day in the hostel.
Now collect the things that you know on a list.
You have the expense E for 32 people per day in the hostel.
You have the expense E + 42 for 39 people per day in the hostel.
(Correct me if I'm wrong.)
20:56
no , you seem right
Now you only need to write down one more fact i.e. you need to make an equation containing E and the information of the minus one dollar per day on average.
Average here means price per person which is the expense divided by the number of people.
I think this should get you started.
give me min , letme now try please
Now, @robjohn, sorry for being so persistent but do you have any idea why Byron deleted his answer?
@Matt Because it was the same as my answer, but referenced outside pages.
Ok. I just had a glance and then it was gone. : )
21:04
Thanks!
@Matt my answer comes 215
@Matt And the here is the link
Aces. Thanks.
@FreakEnum hold on, let me calculate it.
@FreakEnum I think I get something different but I might have got the sums wrong. Can you tell me the equation containing the one dollar difference information?
(Does really no one fancy a very short uniform convergence question? T_T)
@Matt tell me answer? mine came wrong I just checked
21:11
@FreakEnum Tell me your equation.
@Matt my second equation was (x+42)/42 = y-1
x + 42 looks good. I'm not sure about the 42 in the denominator. You started with 32 people and you added 7, how many do you have?
@Matt no we started with 35 people
Then 32 was a typo?
my god , my initial Q has typo , initial number of students are 35
21:17
Well then using the following equation
$$ \frac{E}{35} = \frac{E + 42}{42} + 1$$
I get $E = 420$
@Matt you're answer is perfect. How did you solve that?
What do you think of this? Is it right?
aah I got it
you compared the averages directly
Yes. Do you think that's correct?
@Matt Yes it is, That seems correct answer even to me :)
21:21
Good : ) Let's hope the signs are all correct, too : )
21:40
I can now answer my own question: I saw the uniform limit theorem stated with the condition that the $f_n$ be bounded. That's not needed.
21:56
I can't believe that I'm that close to the 20k and it's gonna take me yet another day!
Are you capped?
Not even close.
Just nothing to answer...
I can't even think of something to edit...
QED
QED
Hi
Hi there.
QED
QED
How's it going?
22:11
I had a nice day today, thanks. And yourself?
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Thinking about printing out lectures notes or buying a second hand book
(All memories of yesterday's set theory failure suppressed. : ) )
What topic?
QED
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complex analysis
but I haven't been able to find a text I like yet
: )
22:17
@AsafKaragila You must be the funniest guy I have ever met. Really.
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I don't understand it
@JonasTeuwen You only say that because you're living with the Dutch... :-P
22:33
Well. If that is the case, I am going to sleep.
Goodnight chumps and chumpettes.
Good night Asaf.
22:58
@AsafKaragila you forgot the grandchumps.
23:21
Good night folks.
23:37
@Matt g'night
I'm left here with the user without a page...
@Skullpatrol: how are things?
@robjohn Fine thanks and you?
I'm a pageless user?
@Skullpatrol Pretty well. I answered a pretty simple question and almost got 10 votes already $\stackrel{\circ\ \circ}{\smile}$
@Skullpatrol If I try to see a page for you, I get the does not exist sign.
@robjohn How do you load this Math Latex thing?
See the starred comment "MathJax Support For The Chat!!"?
Its' too complex for me
all I see is dollar sign symbols etc
23:43
Try the alternate link at the bottom.
Do you see the starred comments at the right of the page?
^^^drag this^^^ to your bookmark bar or right click on it and add it as a bookmark.
@Skullpatrol can you do that?
I'll try...
done, now what sir
@robjohn Where is the book mark bar in chrome?
@Skullpatrol I don't have Chrome, so I am not sure.
@Skullpatrol Does right-clicking bring up a menu in Chrome?
Yes, but no bookmark
23:51
Are you on a Mac or a PC?
and you can't find a bookmark bar on the window?
Intel with windows vista
Take a look here
There is no bookmark bar on the chrome browser if I use the IE browser it has a big star on it
@robjohn Ok
did that help?
@robjohn So now I have a bookmark bar across the top.

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