@SimplyBeautifulArt If I remember you are still in high school right? That was very bold of you to offer to do the calculus thingy. Great job man!

I'm waaaaay past calculus but if you want any help at any point feel free to ping me. I'm usually not busy on the Fridays or weekends if you want someone to help 'moderate' the discussion or something.

just an offer

i'm not the teaching sort

but since we're friends I'd have no problem helping out

@Typhon You can do that simply by stopping into the chat room occasionally.

@SimplyBeautifulArt you're welcome

ok maybe not a congratz

but considering I'd be nervous as heck, that's great that you want to try doing that.

:-)

@Typhon Care to talk about the inaccurate post of yours, which represents your issues, not mine, posted yesterday on "discussion re ed opportunities at MSE... blah blah blah". Every time I think we're friends, you sabotage the friendship by making inaccurate accusations about me. Perhaps I should respond there about you and all your suspensions, how you've harassed me, your habit of over-flagging, and your habit of being harsh and rude in your comments?

If you want to "suck up to" @SimplyBeautifulArt, and/or are smitten by heather, that's fine by me. I have no problem with that. Just don't trash me once every two months, or more frequently, and plant lies about me with your "other friends" in other chats.

@Typhon I'll speak to you no more, because you habitually misconstrue my comments to you, or worse, put words in my mouth. I will only respond when you make dishonest statements about me, and next time I'll come equipped with links to your "confession" to the mods in the mod chatroom, and your solicitation and efforts to delete questions and answers you've posted, because, you were "lying" and "wanted to come across as smart." And then click, 180 degree turn...

@Typhon You repeatedly make provocative claims that trash me. With no merit. I have more self-control than you do. But if needed, I'll expose you and your history on MSE, in chat, on meta, etc.

@SimplyBeautifulArt How are you?

@amWhy I am by no means smitten lol. As I've said since amin started, I'd be interested in the project. Sorry if it sounded like we were talking trash about you earlier, and I don't really chat with many people outside all of the chats you already visit? Save the main math chat room and Kik.

@amWhy I'm good, refreshed, always a good feeling after the shower.

@SimplyBeautifulArt I never said as much: I was continuing my comment to @Typhon, and addressing him. And even then, I addressed (or meant to address hime: "If you ..... or are smitten by heather... no problem." I didn't state that he was in fact, smitten.

@amWhy Oh haha, okay. I was fairly confused for a bit xD

@SimplyBeautifulArt Ahh, yes... that "post-shower freshness".

Huh, 10 or more of my meta comments have 5 or more upvotes on them

@SimplyBeautifulArt Ah, yes, I can see why it could be confusing, especially having pinged you...

@amWhy Do you happen to know when infinitely many linear equations of infinitely many variables are solvable?

@SimplyBeautifulArt Not bad! I know you saw math.meta.stackexchange.com/questions/26934/…; I just hope my comments below arjafi's "answer" there will have consequences. Arjafi can be pretty intolerant of criticism.

@SimplyBeautifulArt Just caught this. What to you mean by "infinitely many"?

@amWhy I was looking at the functional equation $f(x)=e^x + f(e^x)$, and by considering analytic solutions, we get something along the lines of $$a_0=f(0)\\ a_n=\frac1{n!}+\sum_{k=0}^\infty \frac{k^n}{k!}a_k$$

where $f(x)=\sum a_nx^n$

@SimplyBeautifulArt What would you call the area of mathematics that deals with stuff like the zeta function?

@Nilknarf Many areas deal with the Riemann zeta function?

Well, yeah

Mostly analytic number theory and analysis from what I can tell

Analysis, that's the word I'm looking for

xD Okay man

I have a fun (but probably easy) problem for you

Perhaps you've heard it before.

"You have a jar of one liter of milk in one hand and a jar of one liter of black coffee in the other. You pour half a liter of milk into the coffee jar, mix up the contents of the coffee jar, and then pour half of a liter of this mixture back into the milk jar. Repeat $99$ more times. How much milk is in the milk jar, assuming that when you mix the liquids, the particles of each liquid become uniformly distributed throughout the mixture?"

@Nilknarf Wouldn't you want to pour only a third of the coffee jar into the milk?

Right... "half of a liter back into the milk jar"

Ah, okay, my bad :)

Well, you more or less want to find $x_{100}$, where $x_0=y_0+1=1$ and$$y_{n+1}=\frac13x_n+\frac23y_n \\x_{n+1}=\frac23x_n+\frac13y_n$$

Yeah

But it would be a lot less messy if you kept in mind that $x_n+y_n=1$

XD

Ah, you are right

Then,$$x_{n+1}=\frac13+\frac13x_n$$

@SimplyBeautifulArt Yup. That's the meta answer to the question I linked to, authored by arjafi, alright. I had meant to say: I just hope my comments below arjafi's "answer" there will NOT have consequences. arjafi can be pretty intolerant of criticism.

@amWhy lol, well, I think there's enough opposition

@SimplyBeautifulArt lol... yeah!

$$x_n=\frac{1-3^n}{6\times3^n}+\frac{x_0}{3^n}$$

So I guess that solves it @Nilknarf

:D

The next problem I'm doing considers what would happen if you have a circle of $n$ jugs with different liquids, and pour them clockwise

Gonna go eat, cya

@SimplyBeautifulArt Ooh... dinner seems a bit late tonight?

But, since I haven't eaten yet, what are we having for dinner? :P

@Nilknarf Hello! Sorry if I interfered in this conversation.

@amWhy Cury + chicken + potatoes + rice

@Nilknarf x.x Oh dear lol

@SimplyBeautifulArt mmm num num