Simply Beautiful Art's realm of calculus and analysis

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Nilknarf

00:25

@Simply Hiya

Simply Beautiful Art

Heyo

I wrote SOAP up

Nilknarf

yay!

show me!

oh, nvm. Found it!

Simply Beautiful Art

Nilknarf

whoah whoah, complicated

Simply Beautiful Art

X'D

It's the simplest function I could write who's growth rate was that fast.

Nilknarf

00:32

geez

Is this your best one yet?

It's hard for me to tell :P

Better than PAIN?

Simply Beautiful Art

WAY STRONGER THAN PAIN

@Nilknarf and no

There is stronger SOAP

Perhaps I'll call it DETERGENT.

Nilknarf

...good luck turning that into an acronym.

BLEACH

Simply Beautiful Art

Bio-Luminescent Extra Array Character Horrors

Nilknarf

Oh god, you're taking a long time to respond. Please don't tell me you're actually trying to turn DETERGENT into an acronym.

Simply Beautiful Art

I did try

I got to the last E and gave up

Don't ask

Nilknarf

00:37

Awwww

so clooose

Simply Beautiful Art

X'D It was horrible

Wanna try expanding some SOAP?

Nilknarf

Ok, but go easy on me

Simply Beautiful Art

The more we rub, the more the SOAP turns to bubbles, and then we count the bubbles at the end x'D

You pick what you wanna work with

SHOOT, I missed a thingy

Nilknarf

Never before in my entire life has anyone asked me "wanna try expanding some SOAP"?

Simply Beautiful Art

it's just one line of SOAP

Which is going to be terrible to fit in, thanks to the horribly golfed MathJax

Nilknarf

00:40

Hey, have you taken physics by any chance?

Simply Beautiful Art

Fixed it

I've taken AP Physics 1 and Mechanics

I'm taking AP Physics E&M

Nilknarf

Did you guys do circuits with resistors and stuff?

Simply Beautiful Art

Yeah

Nilknarf

We're doing that right now

Simply Beautiful Art

Nice

Nilknarf

00:43

and I love it :D

Simply Beautiful Art

:D Yeah same

You in AP Phys 1?

or 2?

and wanna try expanding some SOAP in less than 20 minutes?

Nilknarf

I'm in 1 right now, but it turns into physics 2 next semester

sure

Simply Beautiful Art

Shall I choose the expression?

Nilknarf

DETERGENT (Dastardly Eventually Terminating Extremely Rapidly Growing Explosive Nerdy Thing)

Simply Beautiful Art

Btw, you think it'll be hard to get a 5 on the AP Phys exam?

@Nilknarf x'D Genious!

Welp, you're taking too long, so we're gonna do $g(\{-1\},2)$

Can't be too big, right?

Looks pretty innocent...

$=g(f(\{-1\},2,\{-1\},2),3)$

Nilknarf

00:50

Blarg, sorry

I'm here

bad internet D:<

Simply Beautiful Art

Oops, some typos

Fixed definition again

:-(

f({-1},2,{-1},2)
= {f({-1},1,{-1},1),-1}
= {{f({-1},0,{-1},0),-1},-1}
= {{1,-1},-1}

Where we use the f({x},...) rule

Not so terrible at all yet...

g({{1,-1},-1}, 3)
= g(f({{1,-1},-1}, 3, {{1,-1},-1}, 3), 4)

Nilknarf

Meh, idk about the AP exam

Actually, I was planning on taking the AP Physics C exams this year as well (I've been doing independent study & calc along w/ my physics class)

I'm more worried about that

How'd you do?

Simply Beautiful Art

f({{1,-1},-1}, 3, {{1,-1},-1}, 3)
= {t, 3, {f(-1, 3, {{1,-1},-1}, t)}}, where t = {f({1, -1}, 3, {1, -1}, 3), -1}

Ugh, what a messy expansion!

This is also the first step that requires us to expand recursively

Nilknarf

yucky

Simply Beautiful Art

It'll probably take up a quarter of the page or so to finish the recursion

And g only managed to expand two steps

@Nilknarf I've been getting 5's

Nilknarf

00:55

Yeah, that's what I thought

Take any AP Histories?

Simply Beautiful Art

@Nilknarf They were pretty easy for me, but you'll probably have difficulty with the physics interpretations of calculus.

I hate history

Nilknarf

I have AP US History this semester

Oh yeah, it's a lot harder

But even a 3 or 4 on an AP Physics C exam as a sophomore should look good on a college application XD

Simply Beautiful Art

But I took
Human Geography,
World History,
US History,
and I'm taking Macro-econ and US Govt

Got a 3 on US History

4's on the other 2

:| Either way, good luck mate

And don't let the physics fool ya

Nilknarf

Yeah, that's pretty much how I'm feeling about histories

Haha ok

Simply Beautiful Art

Now an interesting challenge...

Nilknarf

00:58

Simply Beautiful Art

Prove that g is total

Nilknarf

total?

damn, gtg

Time to wikipedia "total function"!

Simply Beautiful Art

$g(x,n)$ is finite for every $n$ and some fixed $x$.

That's what I challenge you to prove

Nilknarf

Oh, yeah

so basically that it's a function

defined everywhere

Ok, I'll try

cya!

Simply Beautiful Art

:P Good luck and cya

18 hours later…

Leaky Nun

19:21

consider the set of increasing functions from N to N under the partial ordering domination

can I embed omega_1 inside?

4 hours later…

Simply Beautiful Art

23:47

@LeakyNun :| Maybe.

Leaky Nun

@SimplyBeautifulArt why that face?

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