Parth Kohli

Sorry, I didn't mean to say that it's a counterexample

I did talk to the professor about this, and he is quite adamant. He asked me to think about the infinite broom and topologist's sine curve (which quite literally is a counterexample) and come up with an answer

I was able to prove this for piecewise continuously-differentiable but I don't see in what sense of the term piecewise continuous does this theorem hold

There's a theorem in my lecture notes that says, "All piecewise continuous curves [in a closed and bounded interval] are rectifiable". Isn't that wrong? Counterexample: $f(x) = x \sin(1/x)$ for $x \ne 0$ and $0$ for $x = 0$

@skullpetrol Hi haha, I didn't expect my presence to be noted

Guess I'm just gonna post this on the main site.

The imaginary part of which is zero

If it indeed is the case, then I should get 2 pi i times the sum of residues over all poles in the region I'm considering

Sorry, the limit.

Will the integral over the semicircular part of the contour be zero?

I'm sure that something similar has been asked on main before, but how exactly do I use residues to evaluate the integral of sin(x)/(1+x^2) from 0 to infinity?

Yeah I read how it works for basically any field, including finite fields.

So much intertwining - combinatorics with complex analysis, complex analysis with number theory, and so on.

And Discrete Fourier Transform is pretty cool. There's a lot of stuff that I think I'm missing out on, and I guess I should pick up on it this semester.

@BalarkaSen I was reading a thing or two about Dirichlet convolution and Dirichlet generating functions.

@BalarkaSen Me neither. I'm just starting out.

you did get in, so have fun, I guess

@BalarkaSen Wishing for a downgrade, are we?

I can see that

@BalarkaSen Idk, analytic number theory is fascinating to me.

No, just take any $a > 1$ in the sequence and consider the $a$-th term after that.

(Unless of course you're adding zeroes to a prime.)

No, it's pretty easy to prove that it isn't possible.

So add 1 forever

Hm, competitive programming isn't truly CS.

Doesn't matter tbh, but C++ (and occasionally Python3).

I've exclusively been doing competitive programming all summer.

Ohhh, I guess he deleted his MSE profile then

@student Hi! (But, like, who are you?!)

I see you're not the grumpy 14 year-old grand-daddy anymore.

And has there ever been a time in your life when that wasn't the answer to the question?

What've you been up to lately?

Pretty good, I suppose

Hello, @BalarkaSen

@BalarkaSen I've been great, and excessively free. Good luck for ISI. :)

Hey @BalarkaSen. How have you been?

Because they want you to work through the problem.

Which class/grade/standard are you in?

Shoot 'em.

This means that we're looking at x in the interval [-2, 0] (since we have the condition x <= 0). Now in this interval, |x| = -x since x <= 0. So it wants to know for what x is f(x) = -x in [-2, 2].

The set of all x in the interval [-2,2] such that x <= 0 and f(|x|) = x

The only point of this problem is to make you work through cumbersome notation. lol

Okay, which part of this is troublesome to you?

Then just use Google, maybe

Sad

Hmm

I think you just answered your own question here. First build an understanding of the underlying notation.

Hm, they are very fundamental to functions. Koi standard textbook pakad le, and then try solving problems.

Do you have any examples of intimidating notation?

@Jasmine Which symbols are you talking about?