@JasperLoy: Ultimately, I'm just trying to annoy you. stopping...now...

Oh heya @Khallil, didn't notice that you were here (don't get mad at me, I'm just really tired)

Haha, no prob! How's your day been @teadawg1337?

@Khallil It just started, so far I'm super bored

@Mathy I'm here now if you still need help

I've made my hat into a shirt!

@Chris'ssis I just saw @Nick picture......My dog says Welcome back too :D my dog In my sisters lap saying hi :

@Khallil What about you?

It looks like the person in your avatar is reaching out to hold a laptop with a star on the cover, @Nick.

(More in depth analysis, coming to a stack chat near you.)

@TheArtist :-)

It's been ok so far, thanks @teadawg1337. ^_^

I'm learning a bit about sets and tautologies and stuff like that.

That's soo cute, @TheArtist! ^_^/

@KhallilBenyattou Thanks ^_^

@TheArtist He cannot compete with dog with glasses but sure, he's nice.

$$\int_0^1 \left(-\frac{x}{\log ^2(x)}+\frac{1}{x \log ^2(x)}+\frac{2}{\log (x)}\right) \, dx=?$$

Dog glasses are soo lame, @Nick.

@Nick :-)

$$\int_0^1 \left(-\frac{x}{\log ^2(x)}+\frac{1}{\log ^2(x)}+\frac{1}{\log (x)}\right) \, dx=?$$

@KhallilBenyattou Exactly. I that's why I said @TheArtist was better than dog with glasses....

Nooo, the dogs removed Prof. Ted saying "Only discrete mathematics count" from the star-list

@Nick hehe :) you meant the opposite in the prev message

You literally just said that he (@TheArtist's dog) cannot compete with the one with glasses but sure, he's (still) nice, @Nick!

@Studentmath I count.

@Balarka well you are discrete

@TheArtist Umm,....uhh.... ok, you got me.

I'm offended. I thought I'm endowed with profinite topology.

It has the word 'finite' in it

yeah well profinite topology is completely algebra. it's almost not a topology ;)

I hoped someone would mention 'infinite' also has teh word 'finite' in it, but ach so - It's topology built from finite groups or so, right?

@Nick ........

more or less @Studentmath. when you get to learn inverse limits, you'll know about it.

you can just google, i think you have enough background in algebra to understand what an inverse limit is

I will give it a try after I solve this question

@KhallilBenyattou how did you rotate your hat? :)

@TheArtist I'm trying to be vague and have double meaning to everything I say. It's not working out.

@TheArtist Show controls!

@Studentmath in short, profinite topology on any group $G$ is a topology with basis being collection of normal subgroups of finite index.

@TheArtist

the motivation lay in inverse limits

@Balarka oh, I actually understand that.

@Studentmath sure ;) you that much background in topology in algebra for sure.

you have made a considerable progress since you have been here @Studentmath

@KhallilBenyattou @Nick Got it ! Thanks :)

@Nick Yep not working

i admire you.

let me give you something more advanced to compute ...

Admire is a strong word @Balarka, but I'm humbled, thanks :) I do feel like I have learnt a lot (and I did), but still much to go

$$\int_0^1 \left(-\frac{x}{\log ^2(x)}+\frac{1}{\log ^2(x)}+\frac{1}{\log (x)}\right)^2 \, dx=?$$

@Studentmath finite groups with profinite topology are boring.

they're just discrete

on the other hand, infinite profinite groups are very cool. $\text{Gal}(\overline{\Bbb Q}/\Bbb Q)$ is a profinite group, for example.

by "profinite group" i mean there's a natural way to define a profinite topology on it (inverse limits, yadda yadda yadda)

Hah. Why are finite groups with profinite topology discrete? Not every element in $G$ forms a distinct normal subgroup.

Oh, I see

@Studentmath basis

Ugh, so bored..... Reputation is so hard to come by, I wanna be able to review first posts already... :(

@Chris'ssis You here?

@N3buchadnezzar aha

Doesn't the topology comes from unions of a basis? @Balarka

yes

I.e. $V\in J$ iff $V$ is a union of some $B$'s in the basis

every open set is union of elements in the basis, i.e.

yeah

I've got an interesting question, y'all.

So for it to be discrete, every element in $G$ would have to be open, i.e. union of some normal subgroups? (all are of finite index as we are in finite G)

mmhmm

@Chris'ssis Se any of the most common integrals missing from here ?

@Khallil D, and if it is 7 than also 7. Or vice versa.

@N3buchadnezzar I think you added a lot of integrals. ;)

What about 3, @Studentmath?

Ohh you got me.

And actually you don't need to turn 7.

@Chris'ssis I just added the most common ones

3 does the trick.

D and 3

why turn 3?

If the other side has D, then false

If it doesn't, turn D

If you see 7, true.

Or vice versa (if behind D is something else than 7, false, then 3, if not D true if D false)

@BalarkaSen What if (F 3) (D 7) (7 E) and (3 B) ?

Then true

Every card with D has 7 on the other side

every

:19162788 Every card that has a D has a 7, the oposite is not neccecarily true

@N3buchadnezzar You turn 3, the other side has no D.

So you turn D.

The other side has 7, so true.

My algorithm works.

Ohhhhhhhhhh, I get it! If turning the fourth and second cards results in the statement being true, then turning the third card is unnecessary because the statement would still be true regardless of the letter on the other side!

That was a good brain teaser

Reverse psychology @teadawg1337

Is there a way of constructing some sort of truth table for this scenario?

No idea. Tried doing some of those when was skimming through Alice in the Puzzle Land @Khallil

It was years ago.

After much fiddling, I concluded there is no generic algorithm to solve these.

W00t, 9 for 9 on flagging posts!!! :D

@M.N.C.E. @Venus @robjohn have you seen this one before?

$$\int_0^1 \left(\frac{1}{\log ^2(x)}+\frac{1}{\log (x)}-\frac{x}{\log ^2(x)}\right)^2 \, dx$$

Sorry, seeing "9 of 9 deemed helpful" makes me feel accomplished somehow

How did you earn Fascinating Ma'am, @teadawg1337?

@Chris'ssis I just saw it

@BalarkaSen I think it has something to do with voting on questions, but I'm not entirely sure

Hrm.

I'm probably wrong though, lol

Today Dr. Sonnhard Graubner makes me lose my temper

@KhallilBenyattou This is a psychological test whose name i forgot. Do you know the name?

Not a clue.

@Venus This man is too popular nowadays.

Sorry, @Nick!

@KhallilBenyattou Please tell me if you find out.

I definitely will!

@Nick Yeah, @DanielFischer-sensei talks about his high quality answers so much in chat room :D

@Venus And his 15 000 quality posts on Aops

@N3buchadnezzar He is AOPS' user too? What else?

@Venus *mentally challenged

He is user here for about 3 months yet his profile views:2,161. Can you believe it?

Lol^^^^^^

Such gold! You can only find that on MSE!

@Venus Whom are you talking about?

@TheArtist It's on -21 Now!!

OH CRAP!!!!! I FORGOT I RECEIVED A SUMMONS FOR JURY DUTY!!!!!!! THE DEADLINE IS TODAY!!!!!!!!!

@Venus Oh Graubner!

@Integrator Our German Doctor.

@teadawg1337 You are Guilty!

@Integrator I gotta admit this made my day....lol I'm still laughing

@Nick His profile says 0 down-votes! and unfortunately 0 up-votes!

The post was deleted for "reasons of moderation"

@Integrator Could he be a robot? Have we seen any traces of humanity from this creature?

@Nick Nah, MIT would build better bots!

@Integrator ... Me Drools.

Ugh.... I'm gonna have to go today. I highly doubt that being a full-time student next month is enough to excuse me from jury duty

It's like people don't even the question sometimes, right @Venus?

@Integrator Idiocy such as this gets preserved. But not Fermat's notes on his last theorem?

It's just the morning for you, is it not @teadawg1337?

That means you still have time, right?

@Khallil mhm, I've got until 4:00 this afternoon, which is 7.5 hours from now

@Nick Fermat wasn't a Doc! :D

Every-time I visit election page I get one up-vote! Is that a bug?

Well played, Ma'am, hat off to you.

@Integrator Really? Or are you just trolling?

@Nick Really!

@Integrator O-Rlly?

I go insane from stress whenever I barely make a deadline...

@Integrator maybe : $$\text{cream}\to \text{more handsome} \to \text{increased self confidence} \to \text{happiness} \to \text{do math in a happier mood}$$

I want to scream right now, I can't take it :(

@DanielFischer Haha

@Nick $\mathbb R$eally!

@teadawg1337 Scream into a pillow. Jump into a cold shower and maybe kill a few people on the street.... in GTA.

Someone downvotes my answer for the first time ever, haha

:O

the first cut is the deepest

@Venus That was just to take your badge!

@skullpatrol Unfortunately, this video is not available in your country because it could contain music, for which we could not agree on conditions of use with GEMA.

@Integrator I don't think I'll lose my badge

@Venus Why?

@DanielFischer :(

@skullpatrol Is it country music?

@Integrator I read that on Meta

@Venus sort of country pop

@Venus Actually you will not loose badge you currently have, But next nice answer wont be awarded to you.

Wait!

@DanielFischer Do you remember my meta post about 10k voting reversal?

@DanielFischer Should that user lose his (nice answer, enlightened) badges?

@Integrator Yeah, I know that

Why I get 2 downvotes for the same answer?

@Integrator I didn't know which you referred to at first, but now I do. If the badges were obtained through outright fraud, they should be removed, as far as I remember.

@DanielFischer Thanks!

@Integrator It looks like they weren't though, so it was probably deemed insufficient evidence for outright fraud.

@Venus I also lost one badge due to that serial down-voting I received :(

@Integrator Really? How come?

I think I know who downvotes my answer, but forget it.

@Venus Here Maybe both Enlightened and Nice Answer :(

@Venus I see two down-votes but can't help! I've already up-voted it ;)

@Venus And how do you know who is down-voting that answer?

@Integrator Don't worry about that, I still have > 3500, haha

@Integrator I've just messed around with someone here. But, that's only my wild guess. I have no proof for that

@Venus Have Fun now!

@Venus There's a way, Open the profile page of the suspect, Note his reputation, Then delete your answer, After some time you'll see change in your reputation (due to deletion). now again check suspect's rep (If it is increased by one that's good for you). Now again un-delete your answer and wait for change in your rep, Now again check suspect's rep(that should again decrease by one), You can do this multiple times to be sure.

@Integrator Does it really work?

@Venus If you have a suspect, it pretty much works, with a little uncertainty. But, unless you get habitually downvoted, why bother who it was?

@DanielFischer I prefer not to, just let it be. I don't wanna have any prejudice to someone

@Venus Yep, it's more relaxed if you don't care about that. (Except of course, if it becomes a frequent occurrence, then it's probably something one should care about.)

@DanielFischer If it happens frequently, I'll raise a flag to get mods' attention. I can't wait to see you become a mod to handle my flags ^^

@Venus I think ted just made the same mistake as Chris's sis in going to the wrong room :D

@r9m You can always ask :)

@skullpatrol Not necessarily, Ted has been to the election room on purpose, so he might just be checking for interesting new developments.

@skullpatrol Set him up :D

Indeed, @DanielF is correct — as usual.

Hello, @Ted.

Hi, sir @DanielF

@TedShifrin

Finally done with grading and assigning grades. :)

@TedShifrin You misspelled sirrah?

Darn it.

I'm trying to find an old question about surfaces in Lorentzian space. I promissed Ivo I'd expand on my answer for him when I had time. I guess I now have time.

@TedShifrin This one?

If $M$ is a module and $N, P$ are submodules, then $(N + P)/N = P/N$ correct?

That was fast, @TedShifrin

@DanielF: You're so handy to have around. You gonna answer, too? :D

Only if $N \subset P$, @RobertCardona - otherwise, what does the last expression mean?

@TedShifrin No, I don't think I could answer it, going by the title.

I was just typing that, @Mike.

You done flunking your students, @Mike?

I finished last night, @Ted

It's everyone else that still has to work today

@Venus he tests my patience frequently

Well, I had an extraordinary number of high grades in both classes (not that I'm getting generous) ...

OK, let $p(x_1) = p(x_2)$. Since $X \to Y$ is galois, there is a deck transformation $h$ such that $h(x_1) = x_2$. It's given that $p(h'(x_1)) = p(h'(x_2))$. This means $p(h'(x_1)) = p(h'(h(x_1)))$. This means $h'(x_1)$ and $h'(h(x_1))$ are in fiber over some point in $Y$. Again, by galoisness, there is an $h''$ such that $h''(h'(x_1)) = h''(h'(h(x_1))))$

Sheesh

So you're gloating mercilessly, @Mike ? Why are you awake at this ungodly hour for a grad student?

The grades on my problems were mostly quite good. Most common errors were the normal sign errors or dropping a constant somewhere. It was only occasionally that people were interestingly wrong, @Ted

I'm always up at about 7...

Interestingly wrong is always good ... you can spend minutes trying to figure out what in the world they were thinking/doing.

Hi @robjohn: I shall try to test your patience even more :D

One of the questions was to evaluate a certain integral. The answer was very simple (think $\pi+1$ simple). Their solution was to write the integrand as a power series, swap integration and summation, and give their final answer as an infinite sum.

@TedShifrin Since you have time, would you consider unginoring me?

It was an entirely correct answer, though, just not what I was looking for...

@robjohn I can relate your feeling now :D

Perhaps a litmus test Professor @TedShifrin?

@skull: Litmus for whom/what?

Wait @DanielFischer it's obvious right?

for what is your decision Professor

@skullpatrol can you test patience with litmus?

@robjohn busted :(

@BalarkaSen What? Haven't been looking, let me scroll up.

that if $p(x_1) = p(x_2)$ implies $p(h(x_1)) = p(h(x_2)$ then $h$ is deck transformation

@robjohn it maybe considered acidic, in that it corrodes the relationship

Well, @robjohn didn't return my "hi," so perhaps his patience is already overtested.

since $x_1, x_2$ are fibers over a single point, there is a deck transformation $h$ s.t. $h(x_1) = x_2$ since $X \to Y$ is galois

wait

@BalarkaSen Slowly, you have lost me on how you denote what. What is the deck transformation wrt. $r\colon X\to Z$ we're starting with?

@robjohn exhibiting basic patience would be the other extreme

@TedShifrin hi... there :-p

We are given a bunch of galois covers $X \stackrel{p}{\to} Y \stackrel{q}{\to} Z$ and $r = q \circ p$

And a self-homeo $h : X \to X$

Are you back to thinking all self-homeomorphisms can be pushed down, @BalarkaSen?

that is already done @MikeMiller

but not "all"

What you originally wrote is what you have: a deck transformation $h: X \to X$ over $Z$.

Don't know why you edited it.

i already have right-exact 1 --> Aut(X, Y) --> Aut(X, Z) --> Aut(Y, Z)

i want to show left-exactness

Last I heard you were trying to write down the last map... did he do that successfully, @DanielFischer?

to do that i have to show that for any self homeo h : X --> X such that p(x_1) = p(x_2) and p(h(x_1)) = p(h(x_2)) implies h is in Aut(X, Y)

yes @Mike

@MikeMiller I'm not sure. He had something that looked good, and I told him to check the details.

@MikeMiller, if $\overline x \in (N + P)/N$ then $x = n + p + N$ for some $n \in N, p \in P$, but then $x = p + N \in P/N$ so we have one containment. If $\overline x \in P/N$, then $x = p + N$ for some $p \in P$, but then $x = 0 + p + N \in (N + P)/N$. What's wrong here?

That @Mike

@RobertCardona Because $P/N$ doesn't make sense if $N \not\subset P$. That's all. What you want to write is $(N+P)/N \cong P/(N \cap P)$.

yet another Californian @Mike ...

free pen!

That looks like something from the 1960s, @Mike.

@TedShifrin Why did MIT erase all of Walter Rudin's great work?

There are lots of us in California, @Ted

They didn't, @skullpatrol. If you followed that conversation to the end you'll see Alec meant someone other than Walter Rudin.

(I'm also not sure why you think Ted would have any knowledge of the goings-on of his alma mater.)

They never had it, @skull. Misinformed was referring to the physicist Walter Lewin, who was recently accused of electronic sexual harassment.

@MikeMiller LEL

But offer ends 2018

I was born in California but moved from there when I was 10, does that count?

He is perhaps most famous for his YouTube videos of dotted line chalk drawing.

I lived there 18 years so far, @teadawg, but I'm threatening to move back in the next year.

Thanks, I though they did it to both @TedShifrin @MikeMiller

Rudin never had anything to do with MIT in his later life, @skull. He was at U Wisconsin for his career. If I remember correctly, Rudin may have been a postdoc at MIT in the dark ages.

@Mike did you look at what I did above?

No, @Balarka

are you willing to?

@TedShifrin yes you do remember correctly

Not right now. Check the details carefully if you think it's right.

I think it's totally right.

[that means it is wrong with probability 1]

it's probably OK though.

@BalarkaSen That's overly pessimistic.

I am struggling with the kernel of the map.

@DanielFischer I am hardly ever optimistic, except when handwaving.

I handwave a lot.

@BalarkaSen That's your problem, you handwave too much. Read less Arnol'd and more Rudin ;)

haha

I agree with that.

Remind me: is "Galois cover" another way of saying "normal cover"?

regular cover

Thank you Professor @TedShifrin for clearing that up for me :-)

it's just a cover which under application of \pi_1 functor takes the fundamental group of the space above onto the fundamental group of the base space