hmmm maybe I should grab the second equation and then solve for x and y there

@usukidoll I get $X_{t+1}=e^{-bY_t/X_t}$

huh ... I got that with an extra surprise

how did 1/k made it through?

@usukidoll because you didn't cancel something along the way

This looks like the work of some crank

@infinitesimalsimplicio The convoluted way they wrote $-\frac1{12}$ seems to agree with you.

@usukidoll Just substitute $kX_t$ for each $B_t$, and $akY_t$ for each $E_t$ and stop changing cases.

@usukidoll as I said; you did not cancel something along the way.

alright I got the correct equations now ^^

yeah I dropped a k in midair

also I can't divide by 0 if x = 0 and applied to the second equation

I have added some more information: math.stackexchange.com/questions/1205836/… @robjohn

Hello @infinitesimalsimplicio @AlecTeal @Nican!! Are you familiar with PDE's and especially with the energy method?? Could you take a look at math.stackexchange.com/questions/1205836/… ??

omg I hate pdes runs

Hello @MikeMiller !! Could you take a look at math.stackexchange.com/questions/1205836/… ??

@MaryStar I am pretty sure it is bad etiquette, read point 2-4 of the chat guidelines

should I take combinatorics or pde ?

I can either take combinatorics or partial differential equation class what do you guys think ?

I am leaning more towards pdes?

PDE @KarimMansour

yeh I think so too

Combinatorics is the one true path to enlightenment Karim.

Do not be lead astray by the evils of analysis.

Hello @AlexanderGruber !! Are you familiar with PDE's??

@KarimMansour Now you have no choice in the matter, the all powerful mod has decided it for you. :)

@MaryStar Never taken a class on it, but I did a physics degree, which is like 4 years of non-rigorous PDE.

pdes are crazyyyy!

your sanity will go out the window trust me I took pdes last semester ughhhhhh

hmmm sets pde question on fire

I am back. I finished my test.

@Owatch congrats on your 100%

I hope so.

I barely finished in time.

heya @AlexG --- nice to see you at long last!

hi mr eyeglasses and @Owatch

Hello.

My hand aches terribly from writing so much.

LOL ... my students feel that way every class I teach, @Owatch ... We professors are just mean, mean, mean.

And I just finished grading differential geometry homeworks, and very much not happy. Average grade of 0.32 on a required problem.

... The questions were reasonable. It just took a lot of writing to do.

Tests are usually about knowing the basics, @Owatch ... but you really need to know them.

Hi @TedShifrin

Thankfully I could foresee strategies that would not work and saved myself some time on a few.

@TedShifrin 0.32 out of how many per problem

However, I'm not much good at seeing what will work either.

That comes from practice, @Owatch. Aren't you glad I yelled at you so much to practice?

out of 1.0, mr eyeglasses

I spend so much time that week doing problems.

and there was only high school geometry in the problem, once one understood it.

Then most people in my course did not finish them all.

And the professor didn't seem to care too much. I

Sounds like a USAMO problem or something

They are going to get bitched at bigtime tomorrow. Plus half the class drank someone's koolaid and completely messed up basic logic.

can anyone explain Big Oh to me in simple words ?

lol

@user3543449: Are you going to $0$ or going to $\infty$?

Going to inifinity

I felt pretty disappointed that all that effort was taken so lightly

So if one function "looks like" (officially, is bounded above by) a constant times another function for large $x$, then it is big O of the latter.

@TedShifrin hi!

@user3543449 if $\lim_{n\to\infty} |\frac{f(n)}{g(n)}|<\infty$ then a function $f(n)$ is said to be $\mathcal{O}(g(n))$ (or as ted says if there is a bound but the limit doesnt exist)

For example, @user3543449, $3x^3+5x^2 = O(x^3)$.

@JMoravitz: There actually doesn't have to be a limit; just a bound.

For example, @JMoravitz, isn't $x\sin x = O(x)$?

i thought you were conspicuously absent from this room

fair enough.

this is much more familiar

me, @AlexG? I'm not around as much because I've given up on chat on the iPad.

And because I'm getting ready to sell my house and move cross-country ...

But you've hardly been here at all ...

$3x^3+5x^2 = O(x^3)$.I dont get this example .

@TedShifrin Yeah, guess I must have missed the ipad and house selling.

Why not, @user3543449? Isn't $5x^2$ much less than $x^3$ when $x$ is large?

Are you going, going, going, back to Cali, Cali, Cali?

Where will you be moving Ted?

And @AlexG, I'm honestly tired of people who come in here constantly to whine to get us to do all their homework for them.

Yup, @AlexG.

Let me know soon, because I need to rent a uHaul to move my surveillance equipment.

@TedShifrin it is quite less

The Phys.SE chat is wondering what $$\int\frac{1}{\mathrm{d}x}$$ is.

@TedShifrin Yeah, that has been a compelling force behind me recent absence. I'm not going to lie.

Then that's what it takes ... For large $x$, $3x^3+5x^2<3.1x^3$, @user3543449

I figured you were tired of me, @AlexG :P

Well, @Ocelo, it's crap.

@TedShifrin Nah really I've just been busy

I hope it's a good busy ... back still doing better, @AlexG?

@TedShifrin Is there no way at all to give it meaning?

@TedShifrin Are you sure though? I was thinking it's $$\int\frac{1}{\mathrm{d}x}=\frac{x}{4}+C$$

None at all, @Ocelo.

I should write an App for StackExchange's chat rooms.

Yeah for the most part.

@Owatch Sounds lucrative.

After you pass your courses, @OWatch, that would be awesome.

Although nobody's done it yet, so it seems awfully difficult.

@user3543449 in particular, when writing $f(n)$ is $O(\text{something})$, we usually ignore all "insignificant" terms and have the coefficient of the something be 1.

@TedShifrin is Big Oh the maximum value n could take ?

Well, it is disconcerting that nobody has made one before. It indicates: A: It's too difficult B: It's not allowed. Or some other reason.

Yes, you could technically say something is $O(5x^2+2)$ but that is exactly the same thing as saying it is $O(x^2)$

No, what's your meaning of $n$? I was using $x$.

Perhaps I will. I have other projects in the works right now I must finish first, and schoolwork ofc.

@Owatch maybe it's that nobody really uses SE on their phone

Well, the SE folks were working hard on apps for iOS and android, etc., for the regular stuff, @Owatch.

It's really hard to deal with chat on the phone. Tablet isn't so bad.

They have a regular App out right now that I use a bit.

It just doesn't support chat.

@Neuro: I assume you're being 6000% facetious.

Me too, @Owatch.

Hello @TedShifrin !! Could you take a look at math.stackexchange.com/questions/1205836/… ??

Oh, I finally got @EnjoysMath's moronic comment ... he is anti-module, I take it.

No, @MaryStar.

@TedShifrin hey ted!

You need to stop this and talk to your own professors.

heya @Stan

@TedShifrin So, @0celo7 has a different idea than me, but my work is this: $\int\frac{1}{dx}=\int\frac{1}{1-(1-dx)}=\int 1-(1-dx)+(1-dx)^2-\cdots$. Then all the ones cancel (naturally), all the $dx^2$ and higher terms die out, and you're left with $\int(1-2+3-4+5-...)dx=\frac{x}{4}$ (by Wolframalpha regularized result for the sum). Seems like perfectly valid physics to me.

How's the differential geometry/tensors coming, @Stan?

@MaryStar Mary, it's rude for you to spam the chat with links like that. I'm going to have to kick you out if you keep doin' it.

Go fly yourself on the nearest flagpole, @Neuro.

Ok.. Sorry. @AlexanderGruber

@TedShifrin My computation yielded $-x(\log x-1)+C_1x+C_2$, but I think I made an error. I'm not sure if $ \frac{ 1 }{ \mathrm{d}}$ is an integral operator.

@MaryStar no prob. You ought to skim the chat guidelines out in the sidebar sometime soon so you don't get surprised by stuff like that.

@TedShifrin Well, I'm planning out my studies. The physics chat people said something similar to what you said....that I shouldn't jump ahead and go in order. So I need to layout what topics I need to study and in what order I should go.

@TedShifrin I've got the order for the physics subjects, but I need to make a similar list of math topics.

I'm still making progress, don't get me wrong.

@Stan, what courses will you take next semester?

There are things called pseudodifferential operators, but that isn't one of them, to the best of my knowledge, and I can't envison any meaning of $1/\cdot$ that makes that an integral operator.

@TedShifrin heheh so that's a no?

It's a "I'm going to ignore you guys," @Neuro

The math community generally is not impressed by the divergent sum of integers = -1/12 crap.

@TedShifrin Well, I have to wait til the fall to take math. i'm resuming school spring term and placement tests are in the fall. I am taking a music, econ and neuro course. My major is Econ, lol. I'm hoping to test into Analysis classes and take some real and complex analysis next fall.

Econ, @Stan? You're way too serious about math.

Well, I love it!

Studying it makes me happy.

So that's why I do it.

But you really don't want to major in math?

You want to do a Ph.D. in econ ... of the mathematical flavor?

Um, I can't imagine being a mathematician My uncle is one.

@TedShifrin The analytic continuation of the zeta function is not impressive?

@TedShifrin And I can't imagine being a physicist either.

I'm fine with analytic continuation. I'm not fine with the total misinterpretations flying around the internet of what it means.

@TedShifrin But that doesn't mean I don't want to learn them. If I had my choice, I'd be a musician. I make awesome music. :D

Bizarre, @Stan. Well, I've had some superb math/econ double majors, but I wonder what'll happen to you ...

Better to keep music for a hobby unless you're extraordinarily talented and lucky. Classical or popular?

I do all of it. Classical, jazz, indian, rock, japanese. I've got one of those photographic music memories.

I just finished my 63 song :)

@Stan: Once upon a time there was a very serious field called mathematical economics. Berkeley had a department of it, and folks at MIT and Princeton did it. It used a ton of differential topology and stable/unstable manifolds dynamical systems. But I believe it's pretty much gone now.

Interesting, @Stan. My dad was a 20th century classical composer. Hard to make a living in music ... unless you're super lucky ... or are a professor and compose not to make a living.

@AlexG: You got too quiet. :)

@TedShifrin Yeah, exactly. That's awesome. There are so many good musicians I've realized.

I've had students who were very gifted performers, but most of them decided to do math or medicine and make music a very enjoyable hobby.

@Ted help

somebody wants me to write them a recommendation letter

LOL

Ah, I had to do something like 20 of those the past few months.

The most I've ever had in a year.

O.O whatttt

How do you want my help?

20 people ... some had to go to 10-15 places.

Well, I've never written one, or even read one

@TedShifrin Just for reference, it was intentionally dumb ;)

Rec for what, @AlexG?

one for a prehealth post-bacc program, one for a scholarship for people with ADHD

That was my original interpretation, @Neuro, but there's a lot of internet idiocy fueled by numberphile, or whatever he's called.

@NeuroFuzzy What?

I've been seriously working on this...

@TedShifrin Have you ever asked your students to write you a letter of recommendation

@ᴇʏᴇs methinks you mean that the other way around

@AlexG: Ordinarily the advice for the first one would be to get someone with more status and experience evaluating students to write. For the second, I think you should be fine. (I have to do one of those for one of my students, too. That's yet another letter.)

I need help not being crazy

@TedShifrin Differential geometry one of the coolest areas of math. And I'm not saying that just because I like you :P I have always thought straight line spaces were BORING. Even when I was little. And then I discovered non-Euclidean geometry and it was like the coolest thing ever.

mr eyeglasses: When we put people up for teaching awards or promotions, we solicit student letters, so probably 50 have written for me over the years.

interesting

Failing that, I would appreciate help with some basic mathematics.

Interestingly, @Stan, I really only learned non-Euclidean (projective/hyperbolic) stuff long after learning differential geometry. Projective geometry in the context of algebraic geometry, hyperbolic really in the context of teaching undergraduate diff geo.

heya @Anon !!

I've mentored the student for 2 years or so pretty regularly, had her in class and then she's kept coming to office hours. I'm pretty sure I can do the second. Do you think I should tell her to find somebody else for the first?

yo

We're all crazy here, @arkamis.

Isn't there an inequality that says something like $|x-y| \le 2 \max |x|, |y|$?

Sure, @Arkamis.

also, do you know any good examples or anything? i'm not sure how to format it.

You can even prove it.

I wish i could. I keep going in circles. halp.

I think this class has actually made me stupider.

hint: |x+y| is le than |x|+|y|

@AlexG: The latter one is really more an endorsement of her work ethic and attitude. Those folks aren't going to make it on the basis of mathematical prowess, other than overall grades ... would be my guess.

(and ofc 2m=m+m)

@AlexG: If you email me at some point, I'll redact names and send you a sample or two of letters I've written.

yeah, i certainly endorse that. she is very impressive.

@anon I keep getting into a circular logic

OK. should I use the email on your MSE account?

@TedShifrin Does non-Euclidean constitute an entirely separate discipline / area of study from differential geometry? I wasn't aware it was that distinct.

@Arkamis let's hear it

The student who asked me to write this month is taking my super-hard honors class, has all sorts of brain tumors and stress. I'm so impressed by her positive attitude and how she loves the challenge. @AlexG

yes, AlexG, that'll work fine.

@Arkamis Then thin about how $|x|\le max(|x|,|y|)$.

I can't reconcile the subtraction

@AlexG: General word of advice: Any time you write a letter of recommendation, don't fill it with numerical data. Of course, it's ok to talk about class standing, with the student's permission, but specific character traits, or particular episodes (a hard problem that the student was interested in, worked on, and cracked), etc., are much more telling.

Put $y\mapsto -y$ in anon's identity

I keep using $|x-y| \ge \left| |x|-|y|\right|$

I love that inequality, @Arkamis, but when you see the inequality going the wrong way, abandon ship.

At this point I'm just rearranging the deck chairs

but I see it now

Because I'm an idiot.

Thanks

@Arkamis For the moment, use a dummy variable, have $-y = u$. Then you have $|x-y| = |x+u| \leq |x|+|u| = |x|+|-y| = |x|+|y|$

Got it

@Stan, sorry got buried here. non-Euclidean is a classical subject that Europeans still take courses in, but American high schools/colleges abandoned them quite a while ago. You can do a lot of that with no differential geometry at all. I have a chapter on it at the end of my algebra book (basically emphasizing matrices and group actions).

Some people gave up on the test and left.

@Arkamis As for the original inequality in question, without loss of generality let $|x|\geq |y|$. You have then $|x-y|\leq |x|+|y|\leq |x| + |x| = 2|x| = 2\max\{|x|,|y|\}$.

Well, @Owatch, good for you for having the confidence and knowledge to do well.

If you had that $|y|\geq |x|$ the proof goes the same way, thus regardless which case it is, the inequality holds

runs away goodnight, @Mike.

If I did well. I do not know.

Morning @Ted

I swear I'm going to get murdered on this exam because I'm going to forget that 2 times 2 equals 4.

And have no idea how to recover that result.

What level exam/course, @Arkamis?

Measure theory

@TedShifrin I felt like my HS math education was lacking and I went to a good HS. It wasn't bad, but I would have liked more of an overview to see what kinds of maths were out there.

Yeah, I thought you were in a graduate measure theory course.

Inequalities are sort of important :P

I wish I could forget that.

I'm actually doing OK with the material now

Good ... Just stop flipping out.

@Arkamis $2\cdot 2 = 2\cdot(1+1) = 2\cdot 1 + 2\cdot 1 = (1+1)\cdot 1 + (1+1)\cdot 1 = 1+1+1+1$ cough

But the problems take me forever

It's hard to get that even in a good university math training, @Stan, sadly.

and 1+1+1+1 is the definition of 4 (just as 1+1 is the definition of 2)

smacks @JMoravitz

(now that I don't smack Balarka any more, I have to vent on someone)

@JMoravitz I forgot the definition of multiplication using the Peano axioms

<---- pretty much abhors Peano

except for space-filling Peano