user19161
12:00 PM
@JohnJunior Nothing, just got home.

Hmm. My improvement to a question was rejected although I have no idea why.

user19161
@JaakkoSeppälä Have you looked at the question's history if possible?

user19161
Probably too minimal or you changed the meaning too much.

user19161
Or maybe someone clicked wrongly.

user19161
12:03 PM
Many possibilities, don't worry about it.

OK. I tried to change Erdös to Erdős as in Hungary, ö and ő are different letters.

user19161
@JaakkoSeppälä Was that the only change?

user19161
Then it was probably rejected because it was too minor an edit.

user19161
When you have less than 2k and want to edit and earn 2 points, try to make the maximal improvement to the post without altering OP's intention.

12:07 PM
Okay. I just like to fix even small mistakes but it seems to me that not all likes to accept those changes.

@WillHunting Did you change your gravatar back to blue?

user19161
@JayeshBadwaik No, it is just the default one.

user19161
@JayeshBadwaik This looks serious. Did you refresh?

user19161
I hope nobody hacked into my account!

user19161
12:21 PM
Chances are something is going on at gravatar...

@WillHunting My computer has been shut down in between. But anyway, I will clearing my browsing history.
Done, still the results are same.
This does not show up in ff though, so there must be a problem on either chromium or some weird relation between chromium and gravatar.

user19161

@WillHunting Ahh, seems like there was a cache issue! Chromium was diplaying cached image of your gravatar.

user19161
@JayeshBadwaik Yes, weird things always happen around me and inside me.

@WillHunting On a lighter note: xkcd.com/936
and a grain of salt for that: h30565.www3.hp.com/t5/Feature-Articles/…

12:45 PM
@robjohn There is a formula that tells us that for any complex matrix $X$, $\det (e^X) = e^{trace(x)}$
where the left hand side exponential is matrix exp and the right hand side the usual one
I am interested to know
If I have a function $\phi$ satisfying $\det(e^X) = e^{\phi(X)}$
Must it be the case that $\phi(X) =$ principal part of log of $\det (e^X)$?

Hi guys

@BenjaLim If $\det(e^{X}) = e^{\phi(X)}$ for all X, then
$\phi(X) = trace(X)$ and hence, you have a unique $\phi(x)$
since $e^{trace(X)} = e^{phi(X)}$
and for $X=0$ then the LHS will give $\phi(X)=0$ and hence, even if we consider the general log $\phi(X) + 2n\pi i$ the equation will not hold for any $n\neq 0$.

@DantheMan no

@JohnJunior Why? How?

1:01 PM
and principle log of $\det(e^{X}) = e^{trace(X)}$

@JohnJunior Hah ok

@DantheMan 1/0 is not a real number.

@JohnJunior So it's imaginary?

@DantheMan Its not defined.
The operation of division by zero is not defined.
You cannot talk about dividing by zeros.

So it's no kind of number. It's not real or imaginary... It doesn't even exist
2

1:06 PM
Yes!

@DantheMan Because no number times 0 = 1.
2

@JohnJunior Yes

@DantheMan Dividing by 0 would mean multiplying by the reciprocal of 0, but 0 has no reciprocal because 0 times any number is 0, not 1.

@JohnJunior Ah. That makes more sense now!

1:11 PM
Therefore division by 0 has no meaning in the set of real numbers.

Yeah

a/b=a(1/b)

Yes

To divide by a nonzero number multiply by its reciprocal.

Yeah!
Ooops
Wrong one
Factor: $3x^2 - 10x - 8 = 0$
There

1:29 PM
I wrote above that you take the principal part of the log
Ah Sorry my $X$ is not invertible

I'm so tired x_x
TIRED.
I can't think.

Sorry I meant invertible

Your X is invertible? Or not invertible?

@DantheMan (3x+2)(x-4)=0
$$\begin{array}{l}\text{We don't need no education}\cr\text{We don't need no thought control}\cr\text{No dark sarcasm in the classroom}\cr\text{Teacher leave them kids alone.}\end{array}$$

@JohnJunior thanks
@JohnJunior Lol

1:40 PM
All and all I'm just another brick in the wall.

Out goes another student loan payment. 49 down, 131 to go.

@EdGorcenski 49k$? No, payments. Monthly? Yep Just a little less than 11 years to go 1:47 PM That is 15 years!! /me weeps softly Yep. @EdGorcenski Is that normal? Grossly what is the percent of the loan payment per month as compared to$4000? Since that is the average american income on wikipedia.

My overall loan is very small compared to the American average.
It is normal for a graduating university undergraduate to have loans on a repayment schedule of 10-15 years.
I am lucky, my total loan balance is quite small (less than half national average), and I could probably easily repay it within a year. However, my interest rate is so low that there is no advantage in doing so, particularly when I have other expenses.
Also, your estimate for the average american income is actually quite high
That number is before taxes, retirement contributions, and health care contributions
The take home number would be about $2800 after everything is considered. @EdGorcenski Oh. okay. 2:00 PM My loans cost me only around$100/month, which is nothing. Most of my peers pay between $300 and$500.

My full undergraduate education was done in around $2000 dollars while the national average income is around$3000 per year. I am not comparing the education, only costs.

It really goes to show how much of a disaster higher education is in this country.

And what a disaster it is to try to read that :-D

@EdGorcenski My personal belief is that higher education in any country with a big, heterogeneous population will be a disaster at some level, under the current model that is.

@JohnJunior Unsure what you mean

2:05 PM
@EdGorcenski The letter spacing?

@JohnJunior What's wrong with the letter spacing?
It looks fine here.

@EdGorcenski On my screen all the letters are unspaced :(

Youshouldgetthatcheckedout.Therearenoproblemshereatall.
heh

2 hours later…
user19161
3:49 PM
Hey guys, anyone knows the answer to this question on ELU? It's about a math joke. english.stackexchange.com/questions/80912/…

user19161
I've not heard this joke myself, so I don't know if there is a standard interpretation.

@WillHunting No clue.
@WillHunting Watch this

user19161
@PeterTamaroff I'll try to understand the Spanish there!

@WillHunting It has subs!
@robjohn

@PeterTamaroff yes?

user19161
3:56 PM
@PeterTamaroff I was referring to the subtitles. Oh my friend is returning from the US in November, so I can ask him to get some books for me from Amazon!

@robjohn How would you go about evaluating $$A\left( \lambda \right) = \int\limits_0^\infty {\log \left( {\frac{{\lambda + {t^2}}}{{1 + \lambda {t^2}}}} \right)\frac{{dt}}{{1 + {t^2}}}}$$ ??

user19161
@PeterTamaroff I'm glad you did not ask me, I can't do any definite integrals now!

@PeterTamaroff it will take a bit of thought
@PeterTamaroff First I'd try $t=\tan(u)$

@robjohn IWait
Maybe differentiation can be avoided.

Let

$$A\left( a \right) = \int\limits_0^\pi {\log \left( {1 + a \cos x} \right)dx}$$

Then with $x\mapsto x-\pi$ we get $$A\left( a \right) = \int\limits_0^\pi {\log \left( {\frac{1}{{1 - a\cos x}}} \right)dx}$$

or

$$A\left( a \right) = \frac{1}{2}\int\limits_0^\pi {\log \left( {\frac{{1 + a\cos x}}{{1 - a\cos x}}} \right)dx}$$

Now, use the Weierstrass substitution, $$\tan \left( {\frac{x}{2}} \right) = t$$

to get \eqalign{
& dx = \frac{{2dt}}{{1 + {t^2}}} \cr

@PeterTamaroff that looks like the reverse of what I was thinking about

4:05 PM
@robjohn D-oh!

user19161
Great minds think alike, but in reverse directions.

user19161
4:24 PM
@PeterTamaroff You always amaze me with the speed of your LaTeX!
2

@WillHunting That's MathType!

user19161
@PeterTamaroff What is MathType?

user19161
Oh dear, pardon my ignorance. I know almost nothing like I said.

@WillHunting Did you watch the video? It is splendid.

user19161
@PeterTamaroff Yes, a little. I will watch again later.

4:28 PM
@KannappanSampath Thanks for asking! It is fuqed.

user19161
Ah, I found out about en.wikipedia.org/wiki/MathType !

user19161
So Pedro was cheating, hehe.

@WillHunting I always lie.

user19161
@PeterTamaroff I am going to lie on the bed now, hehe.

@WillHunting Go lie while you lie about laying.

user19161
4:32 PM
@PeterTamaroff Now I am confused. You may lie with me if you want, hehe.

@WillHunting Confused is good.

5:04 PM
@WillHunting Dude Amazon ships to almost every country I think.
It ships to mine, that atleast I am sure of.

5:26 PM

6:03 PM
Please, could someone give an example of a concave function? (or maybe a graph)

6:17 PM
@unNaturhal Sure. Why?
@unNaturhal You know what is the easiest way to remember?

@PeterTamaroff Oh, I got it... I had just trouble in distinguish a concave function from a convex one :/

Given a function $f$, the set $\text{epigr}(f)$ (the epigraph of $f$) is the set consisting of all ordered pairs $(x,y)$ such that $y>f(x)$. That is, just shade what's up the graph of $f$.
$f$ is convex if $\text{epigr}(f)$ is convex, and it is concave if $\text{epigr}(f)$ is.
Now, a set is convex if it contains all lines joining the points inside them, yes? It is concave if it's complement is convex.

@PeterTamaroff Yeah.. my trouble was just about what "concave" and "convex" mean graphically

@unNaturhal OK

@PeterTamaroff Thank you very much :)

6:21 PM
@unNaturhal You're welcome very much.

Hi folks

@JohnSenior What's buzzing, Johnny?

@PeterTamaroff Not much maths - been driving new car :)
How are things with you?

@JohnSenior Oh, nice! I'm good. Advancing with Apostol's and Spivak's Calculus simlutaneously. I will become a monster sooner or later.
@JohnSenior What car, can I ask?

6:29 PM
@PeterTamaroff Excellent!
Honda Civic

@JohnSenior My folks have one, but it is an "old" version.
It is a nice car, though.

@PeterTamaroff I had the old version too - until this morning - I love the new version

@JohnSenior, hi.You were right. I was worrying too much about books than actually doing them. Working through Herstein, I now believe it is a gem

I've been trying to get to grips with a problem that Will Jagy told me about
@Steenrod Yep - a real classic. A bit old-fashioned these days, but still an excellent book

@JohnSenior, when it comes to organization, it is much better than Artin.It has great exercises and although it contains less material, the material is strong. My only worry(not something to worry about just now though) is its field theory.

6:34 PM
@JohnSenior This one?

@PeterTamaroff more like this one - looks like a 3-door, but actually has 5 :)

@JohnSenior, there is one reason I hold a grudge against you Englishmen.You went away from India but left the Tripos style exams to torture the high school kids.
:P

@Steenrod ah yes - I don't think Herstein goes very deeply into fields and Galois theory
@Steenrod probably right! But India was free to ditch those styles of exams :)

yep, well said
:D

@Steenrod I am old enough to remember those sort of exams too

6:40 PM
@JohnSenior Tat looks amazing!

@PeterTamaroff Will told me about a rather interesting problem about binary quadratic forms (with an additional cubic term) that he hadn't managed to solve completely - not sure why he thought it worth telling me about it =, though :)

@JohnSenior Do tell me !

@PeterTamaroff We drove it over 120 miles today - first time I ever drove a totally new car - it was great

@JohnSenior 120mph or 120 miles distance? =P

distance :) it is not legal to go above 70 in the uk

6:42 PM
@JohnSenior, when did Cambridge initiate exam reforms?I am interested to know a bit about its evolution from an institution of eternal torture to a smarter system.

@PeterTamaroff going to have to eat - and watch England play football shortly

(ok, I now believe I should let Peter and you complete your conversation)

@Steenrod I really don't know the answer to that one, sorry
@Steenrod no problem - quite happy to talk to 2 people for a few minutes longer
most people here do that - it is not too difficult to keep track of conversations by the links

@PeterTamaroff, are you in college?

@PeterTamaroff @Steenrod - must go - back later

6:56 PM
@Steenrod Yes, why? I mean not know. I study there.
@Steenrod What's with the room?
Gotta go. Be right back.

7:28 PM
Hi
I really need someone who can do knot theory.

I can do many things other than theory!
-crickets-
I'll be here all night, folks.

Well then: help me compute some knots!
You look bored.
Never mind. When I did Bohr sets no one helped me either and I had to figure it out all on my own : /

But I do know plenty about terrible puns.

Poor me.
No, I really want to do this damn knot.

7:33 PM
/pours @Matt a beer.

: D

@Matt So what do you have to do?

@PeterTamaroff Have you found the difference in meaning between : and |?

@JohnJunior Nope, I had social studies today. =P
@JohnJunior Is it a matter of life or death?

8:17 PM
@JohnSenior Do you like questions about how mathematics is expressed in English?

@JohnJunior Not a great deal - but do you have one in particular?
(actually - sometimes I do find such questions interesting!)

@JohnSenior Here.

there is a special place in hell for people who pick usernames which are not 2-character--uniquely-tab-completable, you know...
2

And what do they do to them in that special place in hell?

@MarianoSuárez-Alvarez Agreed - Since Junior has broken this rule, I feel I might have to metamorphose myself again soon :)
@JohnJunior Sorry - I don't think there there is anything useful I can add to that one

8:24 PM
@JohnJunior unspeakable, unspeakable things!

@JohnSenior No problem, thanks for looking :)

@MarianoSuárez-Alvarez Hola
@JohnJunior That was for Matt. He wanted to knot.

56 mins ago, by Peter Tamaroff

@JohnJunior lovely :)

@JohnSenior thanks :)
@MarianoSuárez-Alvarez What does "2-character--uniquely-tab-completable" mean?

8:34 PM
@JohnJunior It means that lazy people (i.e. mathematicians) like to be able to type just the first 2 letters of someone's name and then hit tab to get it completed by the software :)
(no offence intended, Mariano!)

@JohnSenior But is you type "@j" the software pops-up usernames to choose?
@JohnSenior Oh, they want it uniquely determined?

@JohnJunior Yep - so it is bad manners for two of us to have the same 2 initial letters in our names :)

@JohnSenior So using uniqueness to your advantage is a matter of having good manners to mathematicians?

@JohnJunior possibly - but I don't think it is a very serious consideration

@JohnSenior Ahh, now the closure property makes sense :)

8:45 PM
@JohnJunior which closure property?
too many things in maths can be "closed" or otherwise

a+b is a unique real number
ab is a unique real number

@JohnJunior ah - ok
have you been constructing reals from rationals?

There is one and only one possible answer: yes.

Hello hello.

8:48 PM
@JohnJunior I constructed the rationals from the reals.
Do you want to touch me now?

@JonasTeuwen Hi there

Hello.
I need beer. I have a Westmalle dubbel in the fridge as we speak.

Some Physics guy posted some video about how to super cool water here.

@JonasTeuwen a "trappist beer" - sounds great :)

"x is a unique real number" is a statement that doesnot make a lot of sense

8:52 PM
@JohnSenior Of course.

nothing can be*two* real numbers

@MarianoSuárez-Alvarez How about a set of two real numbers?

a set of two real numbers is not two real numbers
it is a set of two real numbers!

@JonasTeuwen Dude.

Depends what you mean with "is".
@MarianoSuárez-Alvarez But a real number is also a set.
I mean...

8:53 PM
@JonasTeuwen What if...

It does not necessarily mean nothing, it just does not say much. More like "x" is a set of one real number (which is a set itself and so on).

ever if you view real numbers as sets (say dedekind cuts, or equivalence classes of Cauchy sequences...) nothing can be two real numbers

A quite Zeilbergerish way to phrase it.

Isn't everything in maths ultimately a set - in some formulations of set theory?

@MarianoSuárez-Alvarez The range of a set-valued function can be seen as two real numbers in some cases.

8:54 PM
then it is a set of two real numbers

It maps to two real numbers or to a set containing two real numbers.
Well, that is what I mean, what do you mean with "is".

nothing can be two different things

"can be" etc.

@MarianoSuárez-Alvarez If only people were more careful about what they said.
@JonasTeuwen Shame on you!

I keep my stand that it is just a matter of definition.
I do agree that it would be a stupid definition.

8:55 PM
you are free to be be wrong :-)

@PeterTamaroff Shame on me? Why? Because I refuse to just accept things others say...?
@MarianoSuárez-Alvarez I surely hope so :-).

@JonasTeuwen I'm just kidding. You should know better.

So what would you say about certain words with multiple meanings?
@PeterTamaroff I should know better what?
Mathematics is not nearly as rigorous as mathematicians claim it to be.

there is a difference between "having two meanings" and "being two things"

@JonasTeuwen Just that we usually joke here...

8:57 PM
the fact that equality is transiytive is at the basis of everything we do

@MarianoSuárez-Alvarez Mariano.

I thought you said "uniqueness" was?

@JohnJunior what?

so that means I can't be "more equal than my brother" after all - darn :(