@Arjun That's cool...

@Arjun Yeah, I had seen that.. perhaps he'd had enough use of this website and left when he felt he got new legs to stand on :D

@Arjun Just...it never occurred to me that things could be represented by sets like that. It just seems so absurd and pointless (at first, at least), if that makes sense.

@RajdeepSindhu You were some seconds late IG.

@RajdeepSindhu @Wolgwang @hansika @HrishabhNayal @LalitTolani @AshishAhuja @Anonymous @AbhinavLenka @Spectre @YashAgrawal @Prithubiswas @satan29 @sai-kartik Any inputs here ^.

2nd line is equal to 1st but how can one think that?

And what's happening after the 2nd line?

@Wolgwang most of the answer is just repeatedly using the trig identities $\sin{A} \sin{B} = 1/2 (\cos(A - B) - \cos(A+B)$ and $\sin{A}\cos{B} = 1/2(\sin(A+B) + \sin(A-B))$

$\sum_{cyc}$: the "cyc" stands for "cycle" AFAIK, i.e for example $\sum_{cyc}f(a - b) = f(a - b) + f(b - a)$

The answerer has split the expression given by the OP into two parts, the first being $\sin^3 a\sin(b-c)+\sin^3b\sin(c-a)+\sin^3c\sin(a-b)$ covered in the first two lines, and the rest of the expression is covered in the lines after the first two lines.. note the full stop at the end of the second line.

Let me call the two parts (i) and (ii) (i.e (i) has been covered in the first two lines of the answer).

(ii) comes out to be $\frac{1}{8}\sum_{cyc}(\cos(3a+c-b)-\cos(3a+b-c))$ which you get by simply applying the trig identities repeatedly. This cancels out with the second half of (i), i.e (i) + (ii) = $\frac{3}{8}\sum\limits_{cyc}(\cos(a-b+c)-\cos(a+b-c))$

Now this remaining part is shown to be zero in the last line of the answer.

"how can one think that" I doubt I would've been able to solve this myself lol so I don't think I can help you here.

@Spectre i don't think he was ever very active on SE

@RajdeepSindhu 😶

that might have been one of the first things i thought while reading math

in 9th ig, tab JEE nahi tha🥲

@Arjun True, he was relatively more active during the days JEE Advanced's result was out, since he had more time on his hands, I suppose.

@Wolgwang Bhoiya mujhse poochke personul attecc kar rahe ho? 🙂

@Arjun 💀

So you're telling me that you thought that $0 = \varnothing$, $1 = \{\varnothing\}$, etc...in 9th grade?!

what the fuck, bro 💀

Anyway, another boring program

editor.p5js.org/TheScientist/sketches/fLtAeEeE4

Milking the hell out of the 3d stuff 🙂

I have no idea why tf this program works or why it took me more than 30 minutes to make this simple shit, but it works 🙂

It's supposed to be a "leg" btw

Press [ and ] to..how do I put it, rotate the full leg (?)

And press ; and ' to rotate the knee, kinda.

858 lines 💀

Anyway, just added constraints, so that you guys don't break the poor guy's kneecaps.

@AshishAhuja Ohk Thanks :)

@RajdeepSindhu Isn't that touched by all basic algebra books?

I recall reading that in Algebra Know-It-ALL: Beginner to Advanced, and Everything in Between in 9th or 10th... 😎 Good-old-days :'-(

@Wolgwang Nope?

First time I heard about it was yesterday 💀

Also, I was an RD Sharma fanboi in 9th and 10th 🙂

@RajdeepSindhu Oh... that's what mom and dad reminds me of often.. freedom right after tons of fighting hours

@RajdeepSindhu I was such back then, but now I'm after good number theorists instead of the school helpers

@RajdeepSindhu I've been working on Pyglet since Christmas

@RajdeepSindhu Man, your profile name is that of a Coldplay song

@RajdeepSindhu It does look like a Minecraft player's leg lol 😂

@RajdeepSindhu stuff like that, not exactly that clear with my notations tho :/

@Spectre i loved this song

last one and the one before her were......next fucking level

the first guy wasn't singing, he was telling what happened to him 🙂

@Spectre I still like RD Sharma's books more than the coaching material stuff, tbh.

@Spectre That's a pretty good name lol. Python's pretty interesting. I have to admit, though, C has been intriguing me more lately, thanks to some computerphile videos (especially those involving Brian Kernighan)

@Spectre ._.

Never listened to it.

It was "TheMastermind01" earlier...a reference to Mr Robot.

Then the Fortnite chapter 2 "The End" live event happened lol and I found it's lore and this character who goes by "The Scientist" pretty interesting so I thought I'd change my username to that till I find a better one.

@Spectre Had to make it simple 😅

@Arjun Demn bro, can't imagine myself thinking something like that ._.

@RajdeepSindhu i could never have made those lens wale graphs too

btw i ordered a book after a looooooong time

a real book

about real analysis

kaya matlab vo JEE ke official syllabus me nahi h

@RajdeepSindhu The coaching materials give more importance to results rather than their proofs, just because the examinees conducting JEE doesn't ask for proofs. Plus, when you're an engineer, you mainly look into application of known results.

@RajdeepSindhu Me too, but only due to lesser reference to it I am slightly detached from it.

@RajdeepSindhu I don't think so though... a neighbour of mine who entered NIT Calicut came around for her term break (she's in the 4th yr now) and she was enjoying her simple hobby of photography!

@RajdeepSindhu Also, my cousin brother who's living abroad tried to complete a 3 yr course (I don't clearly remember which one, but I remember that he had a small course back here in my state to learn accounting as well) ; and he did so! That's the toughest sort of commitment to escape in life, na?? If we're ready to take such effort, each and every one of us will live on a higher place in life

So basically, what matters is commitment

Anyway, good night!

Is it solvable?

Assuming the infinite tetration to be y, it's indefinite integral is 1/2 x^(2xy) according to Wolfram alpha

@Anonymous no idea how to but ig this has a finite value

log leke?

deep

@Arjun Not really, already tried.

@Anonymous by any chance is the answer zero?

@AshishAhuja How?

@Anonymous no I was just taking a guess, now that I think of it it probably isn't zero.. I just noticed that 1^1^1... = 1 and 0^0 = 1, so thought that maybe with a substitution we get an integral with the same limits, so it would be zero... which would obviously be wrong, sorry.

Seems like a pretty tough problem.

@AshishAhuja 0^0 = 1!? Isn't it undefined? (Or kind of indeterminate)

@Anonymous idk much maths..but it seems to be unsolvable..but you may get an approximate answer by using the formulas mentioned here:

en.m.wikipedia.org/wiki/Numerical_integration

@Arjun legends legends everywhere

i've got a total of >100 reputations finally :')

@hansika ._. we've got quite a few here as well(not me for sure)

no words left

@Arjun yeahh..righttt