@Sha !!!

our limits (not "insure" versus "ensure")

oh, on the thought process?

okay wait wait let me check it

maybe I know him, but just not the name:P

you're telling me you don't know big shaq death grips?

@MikeMiller leftbook is pretty good

yes

uhm, I'm afraid not

he has 2 channels

i think

a big one and a small one

@Sha whaaaat

LOL

what

also found another typo

he had 3, the other was a meme channel

it was amazing

"your are"

WAS?

did the channel like decease?

or is that the media thing

you were talking about

do you have an example of another problem where i have to do this upper bound thing

no i mean Fader made a hate stinkpiece against him and he decided to shut it down

oh lol too bad

You need to know Fantano better, he's the best music reviewer in the game/best teeth in the game

let me give you a review

@Meow: In almost all the exercises you need to.

yes please

@ShaVukila Try this

let me try this one

ok he seems strangely familiar to me

@Meow: Except for 1, 2, 3, I think.

the melon is very familiar and friendly

did he ever review eminem's music? because that's where I remember him from:P otherwise, never mind

$\lim_{x\to 2}x^2 +5x-2$

very likely

my problem is

Yes, @Meow, that's an easier one to do.

I don't listen to conventional music, generally

so I know none of the artists he reviews

or their albums

so I guess that's why I never bothered watching him

just start looking at a review regardless of if you know the artist :P

hmm

the thing i linked is very funny

$|x^2 + 5x - 2| < \varepsilon$

but I will miss so many references?:P

after you're done i'll link you something from his meme channel (reuploaded version)

which i found hilarious

haha alright

@Sha The thing I linked is funny regardless of any references

What, @Meow?

oops

And try to write the sentences as I did, as well.

Why don' t you work on it before you type?

so i can tell the limit is gonna be uhh 22

alright one sec

12*

@Balarka okay this guy just really makes me want to listen to conventional music just so I can enjoy his vids in its full glory:P

If you start doing the algebra, Meow, you'll find out soon enough if your arithmetic was wrong.

is the limit not 12?

@Sha you probably don't want to listen to Lil Dicky

hahahahahah oh I do. the worse, the better

it's ranked Not Good/10 in his ranking system

anyways

i did the math i thnk

$|f(x) - L| = |x^2 + 5x - 14| < \varepsilon$

I want you to write me your final nice sentences.

okay so we have a $\varepsilon > 0$ given

@BalarkaSen He might be the best music reviewer but his reviews are not good

we need to find a $\delta > 0$ satisfying other half of $\varepsilon$-$\delta$ def

He is wrong about music imo

-10 for cheating @Meow. :)

I only care about him for the memes @MikeMiller

k

we need an open set of $x$'s around $2$ such that $|f(x) - L| < \varepsilon$

I don't listen to half the music he reviews and he doesn't like half the music I listen to :P

so

excuse me, not containng 2

anyways, so to satisfy that condition we need $|(x^2 + 5x - 2) - 12| < \varepsilon$

i should write but i really just want to read

i don't have any reading backlog though

but this is some quality review

when you simplify and factor you get $|x+7||x-2|<\varepsilon$

My advice, Meow, if you follow my patterns. Forget about writing the $<\varepsilon$ until the very end.

ignore my epsilons

we need a bound on $|x-2|$ to control $|x+7|$

@BalarkaSen have my star

let's pick $0 < |x-2| < 1$

$|x+7| \leq |x-2| + 9 < 10$

which is our bound on $|x+7|$

so we also have the requirement that $|x-2| < \frac{\varepsilon}{10}$

@Ted if you're given a closed subset of R^n with smooth boundary and a closed form on this set, is it necessarily the restriction of a closed form from a small neighborhood of your closed set?

and so our $\delta = \min(1, \frac{\varepsilon}{10})$

does that look right

Someone asked this, here I think, but I'm not quite seeing it

What does it mean to have a smooth function or smooth form on a non-open subset, @Eric?

Now right the final sentence, @Meow. Suppose $0<|x-2|<\delta$ for your $\delta$. Do the estimate.

i don't understand in what sense the form is smooth on the boundary of the set

It has to mean local smooth extensions.

what do you mean, like show that all the $x$ satisfying that satisfy $|f(x) - L| < \epsilon$?

Right. Copy my template, @Meow. I wrote it 4 times for a reason.

In which case the answer to the question becomes obvious, right?

I would define it to mean that in coordinates it's coefficients functions are smooth in the usual sense of functions being smooth on a manifold w boundary

Indeed, @Balarka.

This is a closed set, @EricS, not a manifold with boundary.

Oh, wtf is it?

when $0 < |x-2| < \delta$, we have

Your original question made no sense, Eric.

I was thinking about something like a closed ball

If it's a manifold with boundary, then you have an outer collar.

Locally, at least

on a chart you're smooth on the upper half plane

and you can extend it bit below

$|x^2 + 5x - 12| = |x+7||x-2| < |x+7| \cdot \frac{\epsilon}{10} < 10 \cdot \frac{\epsilon}{10} = \epsilon$

I'm dumb lol

how does that look

Superb, Meow. :)

I looooooooove Concrete Mathematics.

im still a little shaky. ill work on a few more after shwoer

thanks as always

Most welcome.

And TAoCP is pretty damn cool, too.

I think my problem was: not thinking

Classic

@EricSilva: Bums like me are allowed to do that.

I am the expert of not thinking

My brain has been fried more than usual lately

And I haven't even talked to you :)

Maybe I'm taking too much math this quarter

@Semiclassical I might need to explain that one. There is a computional proof that feels like vodoo magic and I was too lazy to work through the vodoo magic computations, so I came up with a conceptual proof

Yay for Stirling numbers.

I would discourage you from overdoing it, Eric.

Next quarter I'll only be taking two math classes as opposed to three so that won't be as bad

@Ted So I guess formally, if $f$ is a smooth function on mfld w/ bf $M$, then there is an open mnfld $N$ with an embedded $M$ s/t $N = M \cup \mathbf N_\epsilon(\partial M)$ and $f$ on $M \subset N$ can be extended to $\tilde{f} : N \to \Bbb R$.

I'm a firm believer in saving grad school for grad school.

@Balarka: I guess I'm thinking of embedded $M$. I suppose we can construct the outer collar abstractly.

Ugh bad notation once again

@Ted what would I take other than grad classes is the question

I did languages and literature and physical chemistry and physics and ...

You told me you had almost a minor in something else.

@TedShifrin Yeah I think we can just take the charts and patch them up abstractly according to the transition functions.

Ya medieval studies

You could take French to know for grad school and to be meducated.

But the Prof who did ancient Germanic/Norse things (which was my main interest) has retired :(

The nerve of him!

Are grad classes the same level as masters classes in Germany? We don't have a lot of grad schools here, so I don't know what to compare them to

Oh I'll definitely take French when it fits

Depends where, @Mathei, but more often courses taken by Ph.D. students.

But in Europe everyone does a masters before Ph.D., so the early Ph.D. courses overlap your masters courses, yes.

I see, thanks

I think I qualify for a dual bs/Ms in math RN but I don't wanna apply for it for fear that it changes my fin aid situation

Other than the charts $U_i$ of $M$ we can just introduce charts $V_j$ that comes from images of balls covering $\partial \Bbb H^k$ in boundary charts $\varphi_j : \Bbb H^k \subset \Bbb R^k \to M$ on which $f$ extends. And then define new transition functions on $\{U_i, V_j\}$ which are the same transition functions on $M$ in the interior charts and stuff on the boundary charts. Doing the gluing (which is a quotient space), that should give the manifold $N$

A little tedious, but should be doable

I mean, most Ph.D. students in the US don't have the background of taking grad courses as undergrads at Berkeley, MIT, Harvard, Chicago, etc., and so they start with graduate work in analysis, algebra, topology, differential equations, etc., and then move on to representation theory, alg. geometry, diff. geometry, PDE, etc.

@EricSilva: Unless you decide not to go for a Ph.D., it's totally irrelephant.

boop

That is good

Meh, there's a better way to do it. Just take $M \subset M \cup_{\partial M} M$; locally extend $f : M \to \Bbb R$ beyond $\partial M$. The extended domain is a submanifold of the double; that is exactly the desired $N$.

@Ted I figured at one point that the MS might make some difference if I applied to foreign schools (e.g. IMPA) but I'm pretty sure I'm not going to do this now

Eric, since foreignly people do masters before Ph.D., that would be a concern.

Yeah this was my line of thought

@MatheiBoulomenos gotcha

That’s about what I had in mind, really

maybe i should just apply for it in case i decide in the end that i want to jump ship and go to Brazil (i.e. become a beach bum)

Somehow, I don't think you'd last long as a beach bum.

back

also Ted did i tell you i joined my schools math league?

nope, but that's cool, Meow

@MikeMiller Iknowright?

Hey, this seems like a good place to ask—where should I read to start learning Tex?

@Ted I come from a long line of beach bums, it's in my blood

And how similar/wildly different is it from MathJax?

I see @EricSilva. The math is an aberration?

(I mean, obviously it has all sorts of formatting options, but is the math formatting reasonably similar?)

@Wildcard: Actually formatting documents, lists, etc., takes some learning.

The math syntax you use here is LaTeX.

@TedShifrin Sweet.

But, how different is LaTeX from Tex?

(And how does MetaFont fit in, or does it really?)

Knuth's TeX is the underlying engine. It's called Plain TeX. Then there's AMSTeX, LaTeX, etc. LaTeX allows the most flexibility for automatic numbering/referencing ... I never learned MetaFont, but people do make up their own fonts and import them to (La)TeX.

@TedShifrin That doesn't surprise me. I'm a pro with InDesign and Acrobat Pro, so I have some idea of the capabilities that I would want in a typesetting program. Anything that would be "quick to learn" I would expect to be woefully underfeatured. (Like markdown, which is great, but not for actual documents that you want to look good.)

my grandpa really liked math actually. He ended up dropping out of primary school (side effect of being poor/indigenous in early 20th century Brazil I guess) but ended up learning algebra from my mom later because it was the one thing he always wished he could do. @Ted, interestingly I didn't know about this until after I found out I liked math and apparently we share a lot of habits despite the fact that i only met him a few times

@TedShifrin Ah, so a key feature of LaTeX is cross-referencing/numbering? And that's not in TeX? That's sort of surprising, actually.

Let me put it this way: is all valid Plain TeX also valid LaTeX? In other words is it a superset of features?

Correct. That was not in Knuth's original. But for articles/books, etc., it's highly useful.

@EricSilva: I had an elderly relative in Russia (my mom's mother's brother, I think) who was a mathematician. I corresponded with him once or twice in high school, but that was it.

@TedShifrin Yeah, that's why it's surprising it wasn't in the original—because he used it for his own books. I wonder if his pre-defined outlines had anything to do with that feature's absence (maybe he didn't need dynamic cross-referencing because he'd already written and numbered the entire outline for TAoCP).

I did my first book in AMSTeX and then realized that any revisions I needed to make required manual search/replace for exercise numbers/references, theorem numbers/references, etc. I quickly converted to LaTeX and never looked back.

finding extended family with similar interests kind of makes me wonder how much of these tendencies are influenced by genetics

In LaTeX you have a package for coffee stains. I think that's quite the unique selling point (There does not seem to be a good translation of "Alleinstellungsmerkmal")

Well, my sister followed my dad and mom into the music/art world, Eric.

Coffee stains? Das hab'ich nie gehört.

i think parents exert a big social influence so it's kind of hard to separate that from what might be genetic or w.e.

on the other hand, I'm the first of my family to do instanton Floer homology

@Mike I lol'd

First in my family, too, Mike.

so Floer homology is not genetic

hanno-rein.de/archives/349

Hysterical, Mathei!

"A lot of time can be saved by printing stains directly on the page rather than adding it manually."

@TedShifrin Thanks!

@TedShifrin So, LaTeX has comparable mathematical support to AMSTeX? Interesting.

There are various books and lots of stuff on-line. I bought three of the books years ago before the internet was a thing.

on the other hand I apparently have similar vocal ticks to my maternal grandfather, he was also a synesthete like me, etc etc, so it was weird for me to hear about all these similarities we apparently shared when i was like 16 and hadnt seen him in 10 years @Ted

Well, which part of the family did your cooking come from, Eric?

both i guess, my parents are both like incredible cooks

oh great

i don't have much interest in being conscious of my family history

Yeah, I've not ever done any of that.