Hakim

@Khallil yup, although I never had an occasion to exploit it

@Khallil hahaha cheater

@Khallil Correct ^^ btw was just testing out my $\rm\LaTeX$ skills

$$\hskip 6em {\require{cancel}\require{cancelto} _\text{psst! over here!}\cancelto{\hspace{1pt}}{\hspace{20pt}}}\style{ display: inline-block; background: url(//i.sstatic.net/NsEYz.jpg) no-repeat center;}{\phantom{\Rule{56px}{85px}{0px}}}\longleftarrow\text{psst! guess what this is!}$$

Happy New Year!!! @all

$$\style{ display: inline-block; background: url(//i.sstatic.net/atLTv.jpg) no-repeat center;}{\phantom{\Rule{50px}{50px}{0px}}}$$

@Vrouvrou happy new year !

Contrary to popular belief, one may show up images using $\rm\LaTeX$, $$\style{ display: inline-block; background: url(//i.sstatic.net/C8nN0.png?s=42&g=1) no-repeat center;}{\phantom{\Rule{42px}{42px}{0px}}}$$

@Anubhav.K was just testing out some $\LaTeX$

@Khallil no problem, haven't checked my email for quiet some time now

@Khallil yeah, have been pretty much absent for the past months, excellent, i wish you a nice new year ! :-) So I guess you finished spivak now?

Hey @Khallil

@Chris'ssis Yes, but do you know how we can evaluate it? I have no idea though.

@Chris'ssis What about this series, have you ever seen it? $$\sum_{k=0}^\infty\dfrac{(-1)^k\left(k+\dfrac{1}{2}\right)\sin\sqrt{\left(k+\df‌​rac12\right)^2\pi^2+a^2}}{\left(k+\dfrac12\right)^2-b^2\sqrt{\left(k+\dfrac12\rig‌​ht)^2\pi^2+a^2}}=\dfrac\pi2\sec(b\pi)\dfrac{\sin\sqrt{a^2+b^2\pi^2}}{\sqrt{a^2+b^‌​2\pi^2}}$$ (the LaTeX code is fine but it doesn't work)

3

30 secs

@r9m Oh, thanks! :-)

@Chris'ssis I have no idea, maybe will have to use a probabilistic argument, no?

@Chris'ssis Do you know how to approach it?

Hi @ForeverMozart

@KhallilBenyattou That's ok, my comment was on the procedure by which you show that $n=q_1m+r_1$ and $n=q_2m+r_2$ implies $q_1=q_2$ and $r_1=r_2$.

@KhallilBenyattou Just recall what the question says: "Show that for any given $m,n$ [...]". So when you found $(q_1-q_2)m+(r_1-r_2)=0$ for all $m$, then it follows that $q_1-q_2=0$ and $r_1-r_2=0$.

Hi @daOnlyBG

@Khallil You're welcome. ;-)

@Anastasiya-Romanova秀 I was before I deleted my FB.

@Khallil As an alternative there's also Abbott's Understanding Analysis.

@Anastasiya-Romanova秀 The days when I had an fb account

@Khallil Tao / Analysis I & II, it's crystal clear and it focuses heavily on intuition although there are no illustrations.

@Khallil Which textbook are you using?

@Anastasiya-Romanova秀 I used to know him, indeed he has some very interesting problems.

@Khallil Not much, I have very little free time these days. What about you?

@Chris'ssis chat.stackexchange.com/transcript/message/19031016#19031016

@Chris'ssis Do you know whether your series diverges or converges? (numerical check seems to suggest the latter)

@Khallil Yeah, as always, how about you?

Hi @Khallil

@Chris'ssis I'm fine, thanks. :-)

Hello @Chris'ssis

@goldPseudo Salam, did this answer your question? regards.

Flags required.

In fact I earn a living by repairing computers and phones (more on the software side).

@infatuated Nope, just a regular guy who likes to self-study.

@infatuated That's not right, okay as a practical experiment, try one month to stop listening to music and see whether it renders some improvements, then come back here. ;-)

Then you do agree that Muhammad knew the best about what can affect our imaan in a bad way, and it wasn't pure coincidence that he prohibited music.

@infatuated I disagree with your previous remark, the best judge isn't the believer himself as his brain can be fooled by the pleasure gained by some activities and thus following it.

@infatuated Who do you think had the most truthful knowledge?

Just launched a new SE Proposal : Physics Educators for those involved in the field of teaching physics, a bit like the Mathematics Educators, if that interests anyone.

Jyrki Lahtonen is running!

@Ashwin Motivation is unreliable, not worth it. It is easy to rely on since it requires no effort to get. What really matters is discipline and dedication, force yourself to work.