Mathematics - 2017-04-21 (page 1 of 2)

Jacksoja

00:05

hi chat

Mike Miller

@Daminark I always thought more as my thing than his.

Daminark

What @Mike?

Mike Miller

@Daminark getting continuous out of smooth

Daminark

His = Ted's?

Eric

hi chat

Daminark

00:12

I was joking with him, he's actually not terribly fond of spending time on that given that there's only a quarter

Hey @Eric!

Eric

What have you been doing in analysis Daminark?

Daminark

Convergence theorems for Lebesgue integration

Our TA has been lecturing

Eric

ah good good

how is she?

Daminark

She's really good

She goes faster on average than, say, Marianna (some people in the class have felt this is a bit too fast, but I don't think I'd say that)

Mike Miller

I like it, but it's all a very general principle that makes continuous results fall out of smooth ones

Daminark

00:17

Yesterday was Littlewood's 3 Principles (more precise version), then monotone convergence and Fatou. Next class is gonna be dominated convergence and then Fubini's theorem.

Next week Marianna will be lecturing again, and if I remember right from office hours it's soon gonna start going the direction of density theory

@Mike That of approximating them using convolution/molification? Or do you have something else in mind?

Mike Miller

just the existence of smooth approximations (and the existence of relative approximations, ie where the function is unchanged on a certain subset); of course you can get that via convolution arguments (and i like those quite a bit)

Eric

it's not a party until someone starts convolving things

Daminark

Lol the proof of Stone-Weierstrass led to Soug's extra stuff on convolution

Which was one of basically 2 times I'm aware of when he went off script

Kasmir Khaan

00:33

Hi chat ! , what is the easiest way to show that a graph does not have hamiltonian circuit ?

Daminark

01:01

Hey @Kasmir, @Adeek, and @Dodsy!

Adeek

hi @Daminark

Daminark

How's it going?

Adeek

good solving problems for final tomorrow

Daminark

Ah, good luck

Got midterms next week

Adeek

thanks :)

u2 next week

Daminark

01:08

Thanks!

Kasmir Khaan

01:26

@Daminark Hey :)

@Adeek Good luck Karim

Adeek

thanks

Daminark

01:38

What'd've you got going on?

Adeek

I am solving stuff about flat modules then on Noetherian rings.

Daminark

Cool! What makes a module flat?

Adeek

@Daminark If applying tensor product always induces for any SES an SES when tensored

or equaivalently

M is exact if whenever $N_1 \rightarrow N_2$ embedds onto $N_2$ then tensor with M is also injective.

Daminark

Sounds pretty neat

Adeek

yeah it is

Daminark

01:54

What classes are you gonna be doing next term?

Adeek

don't know yet

hopefully something geometric + something algebraic

+ research

Daminark

Ah, sounds fun

Algebraic geometry?

Adeek

yeah or maybe more like differential geometry

@Daminark If more differential geometry and algebraic geometry is offered then I will take both

Daminark

Nice

Little Rookie

02:11

Hello all, when it is said that a series $\sum_{n=1}^{\infty}a_n$ converges absolutely to $a$,

Does it mean that $\sum_{n=1}^{\infty}|a_n|$ converges and $\sum_{n=1}^{\infty}a_n = a$ ?

Daminark

I parse that as saying $\sum_{n=1}^{\infty} |a_n| = a$

Little Rookie

i have a theorem that says if $\sum_{n=1}^{\infty}a_n$ converges absolutely to $a$ and $\sum_{n=1}^{\infty}b_n$ converges absolutely to $b$, then $\sum_{i=1}^{\infty}\sum_{j=1}^{\infty}a_i b_j = ab$

Dodsy

02:25

hey @daminark sorry I didn't reply. I fell asleep watching hockey.

Kasmir Khaan

02:38

what is the easiest way to show that a graph does not have hamiltonian circuit ?

Little Rookie

@Daminark someone replied to the question on main, its the other definition

It's a shortened combination of "∑∞i=1an∑i=1∞an converges absolutely" and "∑∞i=1an∑i=1∞an converges to aa".

Daminark

02:56

Lol it's fine @Dodsy

And @Little I see

Dodsy

:)

Kasmir Khaan

03:28

hi @TedShifrin

Dodsy

03:47

Ted

you're up late.

@TedShifrin I'm going to watch your lectures, I totally forgot you mentioned you had them up online!

I love how you tell students "I don't like that"

Ted Shifrin

I'm in CA — hardly late !

Hi @Kasmir

Kasmir Khaan

@TedShifrin Nice what are you doing in cali ? =p

Ted Shifrin

Nothing.

Kasmir Khaan

Okay =p my exam on complex analysis went really well

We get the results on 25 th =p

Ted Shifrin

Oh, well, I hope you're right.

Kasmir Khaan

03:55

btw Ted how can we tell if a graph is not hamiltonian just by looking at it?

Ted Shifrin

I don't know graph theory.

Kasmir Khaan

Okay thanks anyway :)

Dodsy

Ted, I feel like when we talk online I have no idea what you're talking about. But when I'm watching this lecture I feel like everything you say makes perfect sense. ;)

Ted Shifrin

One of you is fooled? :)

Dodsy

I find it strange that in my calculus courses coordinates were written (x,y)

arctic tern

03:59

my comment got deleted from n-category cafe :/

Ted Shifrin

That's standard, Nate.

Was it decaffeinated, tern?

Dodsy

oh but in your lecture it says that the coordinates of vector x are written as [x1 x2]

but they're written horizonally.

vertically..

my dad doesn't know his rights from his lefts and I don't know my horizontals from my verticals..

Ted Shifrin

Right, for reasons that become clear later ....

Dodsy

oh okay

:)

What are you doing in california?

accepting some prize?

:D

Ted Shifrin

I moved here almost 2 yrs ago?

Dodsy

04:05

Oh wow, I'm an idiot.

Ted Shifrin

rolls 5 eyes

Dodsy

rolls 50 eyes

Ted Shifrin

Wow, and @Balarka missed it!

Dodsy

How long do you think you should take to read a math textbook? How many hours should go into absorbing the information from a technical text?

Like if I bought your multivariable textbook.

Ted Shifrin

You have to read with lots of paper and pencil and work things out step by step for yourself. Not to mention exercises ....

Paul Plummer

04:09

as long as it takes to get as much as you want/need...

Dodsy

....

ellipses

@PaulPlummer I don't think that's necessarily a good way of looking at a subject.

Paul Plummer

What way?

Dodsy

That you should only learn what you think you want or need and discard the rest.

Paul Plummer

So learn everything? Good luck with that

Dodsy

Well, no.

But it's still a strange way to look at techniques for self studying.

Like if you get a textbook for your class on calculus are you only going to open it to find the homework problems your teacher told you to do?

Paul Plummer

04:14

Well if you stop wanting to learn diff geo, or multivariable calc, why would you still study it? Depends how interested I am in it

I might not even do the homework

Dodsy

alright I'm off guys

cya Ted.

Ted Shifrin

Cya.

Kasmir Khaan

@TedShifrin can I give you few of the questions and my answer to them on the exam we had ?

@TedShifrin so you tell me if i did good or not =p solution is not up yet

Paul Plummer

04:30

@Dodsy Asking how long should it take to read a textbook isn't exactly a good way to think about learning a subject btw. Why does it matter how long it takes or should take if you actually want to learn it? Learning takes a long times, and has many stages.

buddhababe

Hiiii

I'm looking to learn about Darboux/Riemann!

Daminark

Just do Lebesgue from the beginning!

Lol jk

buddhababe

Haha. Okay.

Insight is hard!

Daminark

It very much can be

buddhababe

04:46

Does anyone know how to find the area of a given region?

@Daminark Thank you for understanding, haha

Paul Plummer

04:59

@BalarkaSen Hello

Balarka Sen

Hi @Paul

I woke up late today

Paul Plummer

What time is it?

Kasmir Khaan

Hi

I need help with hamiltonian graphs anyone know graph theory ?

Daminark

Hey @Balarka!

@Kasmir Unfortunately, not yet

Kasmir Khaan

:)

buddhababe

05:02

i studied a lil' hamiltonian

Kasmir Khaan

Is there an easy way to find out that a graph dont have hamiltonian circuit?

Balarka Sen

@PaulP About 10:30

Hi, @Daminark.

buddhababe

@KasmirKhaan noooope

Balarka Sen

@arctictern did you stick to the n point of view?

Paul Plummer

Have you seen McShanes Identity? @BalarkaSen

Balarka Sen

05:17

I haven't. That's pretty interesting!

Paul Plummer

It has been used to calculate the volume of moduli space of the punctured torus

Balarka Sen

Looks a lot like Selberg's zeta function (analogue for Riemann zeta for hyperbolic surfaces)

buddhababe

You can puncture a torus?

Woahhhh

Paul Plummer

Well poke a hole

or remove a point

Alessandro Codenotti

Hi chat

Kasmir Khaan

05:25

hi @AlessandroCodenotti

Paul Plummer

Hello

Balarka Sen

Hi @Alessandro

Paul Plummer

Thinking about anything cool @BalarkaSen

Balarka Sen

I should be learning Morse theory of foliations but I am procrastinating.

Daminark

Hey @Alessandro!

Balarka Sen

05:34

@PaulPlummer Learn't Thurston's theorem that any 2-plane distribution on a 3-manifold can be homotoped to an integrable distribution. The proof is a little bizarre, but interesting.

Paul Plummer

That does sound cool. Is it looking at space of foliations and figuring out how to do morse theory on that space or is it like a morse function where you are constant on leafs, or something else...

or is this the theory where you don't require critical points, but weaken to "critical submanifolds"

Balarka Sen

It's like Morse theory but with leaves of the foliation, yeah. So for usual Morse theory you'd foliate by the preimage of the Morse function.

(The second comment about Thurston's thing is disjoint from this though)

Kasmir Khaan

Construct a simple graph with vertices {A, B, C, D, E} that has an Euler trail, the degree of A is 1 and the degree of B is 3.

What is the edge set?

Anyone know how to answer this ?

Tim The Enchanter

06:27

@KasmirKhaan A graph is eulerian if it has at most two odd vertices (A and B), so it ought to look a bit like this. imgur.com/a/Nwo85

Im not sure what an edge set is though

Kasmir Khaan

@TimTheEnchanter thank you :)

Edge set is just naming those example if you have an edge from vextex a to b you put (a,b) , (b,c ) ect =p

Tim The Enchanter

Ah well, I've always been one for the pictures.

Kasmir Khaan

Its just a way to work on computer =p easiar to put them in edge set notation =p

Dodsy

08:57

@PaulPlummer You're clearly one of those types of people who believes he is the smartest person in the room. I believed at the time that my question was a good question, as I do now. I was asking Ted how long it generally takes to study through a text book. You believe it is a stupid question, and good for you. I thought your answer was stupid. You're entitled to your opinion, but I did not expect to be belittled for my question. As I'm sure you didn't expect to be belittled for your answer.

Balarka Sen

09:25

@Dodsy I don't think Paul belittled you for your question, neither can I see where he called your question stupid. I agree with Paul's answer, and I believe anyone in this room would agree with his answer to some proportions. On the other hand, you are the one who's attacking him personally.

SteamyRoot

09:39

@Dodsy Seconding this ^. And, about your question: different people study a book in (vastly) different ways. Some people write down a lot and some don't; some people feel the need to make way more exercises than others; some people just need more time to grasp something; etc. I don't think there is a meaningful way to assign a length of time to this process of learning.

In my opinion, it is more meaningful to study some chapter at your own pace, in your own way; and then pick some exercises and ask yourself: "If I understand this chapter, can I solve this exercise, and how long should it take me?".

Alessandro Codenotti

It also kinda depend on the textbooks, there are some that would require me various years for sure

Tim The Enchanter

I'm trying to prove that If $w= z^2 + az + b $ and $\forall z \in \mathbb C , |z|=1 \implies |w|=1$, then $a=0, b=0$ or $w=z^2$. I have a geometric argument, $w= z^2 + az + b $ comprises of a linear shift by $a/2$, squaring, and a linear shift by $b - \frac{a^2}{4}$. I'm pretty sure as squaring a circle in the complex plane deforms the circle so as to render it impossible to map onto the unit circle at origin, so $a=0$ from which $b=0$ follows.

I'm not sure how to make it rigorous.

Also $a,b \in \mathbb C$

Any help would be appreciated

LegionMammal978

10:52

Question: You are given an urn with a unknown (finite) number $N$ of balls in it, each of which is a different color. You can sample $4$ unique balls from this urn and replace them. How can you determine, with at least $0.999$ (or even better, $1-\epsilon$) probability, whether you have sampled all $N$ balls yet?

SteamyRoot

12:03

@TimTheEnchanter I'm not sure this method would work or would be easier, but my first attempt would be as follows. There are $4$ real unknowns: the real and imaginary parts of $a$ and $b$ - hence we could try to get $4$ equations. So take $z = 1, -1, i$ and $-i$, and use those to find the unknowns

vin

Hi, are graph theory books from mid sixties to mid eighties still relevant? By studying from them would I be wasting time on trivial or superseded concepts? There are some known classics available at low price, so want to know if they are worth buying.

user193319

Hello. Here is a problem I am working on: Let K > 0 and f : R -> R be a function satisfying |f(x)-f(y)| \le K|x-y| for all x,y \in R. show that f is continuous at every point c in R. So, with respect to the definition of continuity, wouldn't choosing d = e/K work to show f is continuous?

Where d and e are obviously taken to be delta and epsilon, respectively.

BAYMAX

12:40

Is $-lim inf = lim sup$ ?

N3buchadnezzar

Hey all =)

Fawad

Hey all =}

N3buchadnezzar

How is it going? ^^

SteamyRoot

@BAYMAX You may want to mention for which $f$ you're asking this

And which limit you're taking

But in general: of course not. Let $f$ be constant $1$, for example

BAYMAX

oh

non negative functions g and $f_{n}$

$|f_{n}| \leq g$

for all n

then this equality

Lim iinf $\int [g-f_{n}] dx = \int g dx - limsup\int f_{n}dx$

@SteamyRoot

I think it applied liminf$\int f_{n} \leq$ limsup $\int f_{n}$ ?

Secret

13:02

Last night dream: Unknown BEAF stuff
Evening nap dream in the car: Measuring a dream's creativity by the status of the city is being built
Short nap because too tired when arriving home, dream: Solving the BEAF expression: 3}}}}}}}}}$\cdots$ }}}}} and seeing weird arrays $\{a \& b () a^m \& b \cdots\}$ where the first one is ordinary and the other one is Legion. Dream is hinting about a cantor normal form analogue of BEAF expressions

Paul Plummer

@Dodsy I didn't mean to come off like that and it looks like @SteamyRoot expands on some of my thoughts on it. I believe you have an honest question but at the end of the day I don't think any answer would be meaningful or satisfy what you "actually wanted".

Maybe you did just want Ted to say 800 hours or something, but I don't think he would ever say something like that because he knows that is not how learning works. And if you look back at his response it does basically say "as long as it takes". I actually think it can be discouraging to set up these time limits, because what happens if you are over, and by a lot?

user193319

Would someone mind taking a look at my problem? Let K > 0 and f : R -> R be a function satisfying |f(x)-f(y)| \le K|x-y| for all x,y \in R. show that f is continuous at every point c in R. So, with respect to the definition of continuity, wouldn't choosing d = e/K work to show f is continuous? Where d and e are obviously taken to be delta and epsilon, respectively.

Balarka Sen

Hi @PaulPlummer

Paul Plummer

@BalarkaSen Hi

BAYMAX

How to put a bar below something in LaTeX ?

$\bar{x}$

$\underline{x}$

SteamyRoot

13:15

underline?

BAYMAX

nice,steamy!

Kasmir Khaan

hi chat

what is the criteria for bipartite graphs ?

BAYMAX

13:33

If a function is montonically increasing does the derivative aways exist?

ComFreek

@BAYMAX Is it continous?

BAYMAX

suppose in closed interval $[a,b]$

yes

ComFreek

@user193319 Yes, this is the standard proof that Lipschitz continous functions are also continous.

BAYMAX

perhaps you meant BAYMAX.

ComFreek

No, this message was in fact targeted at 193319.

BAYMAX

13:35

ok

ComFreek

@BAYMAX I think so.

BAYMAX

ok

Secret

derivatives don't exists at cusps at e.g. broken line increasing functions?

ComFreek

Yep, you are right. My bad.

BAYMAX

yup,that is nice one there!

Secret

13:50

more extremely, I wonder if it is possible to have a monotonically increasing weistrass looking function such that it is nowhere differentiable

BAYMAX

I heard some theorem like it can be non differentiable at countably many points

Kasmir Khaan

Construct a simple graph that is a tree with vertices {P, Q, R, S, T, U} such that the degree of P is 5.

Anyone can give me a hint?

Secret

15

Q: Monotone+continuous but not differentiable

Is there a continuous and monotone function that's nowhere differentiable ?

real-analysis

It appears countably many non-differentiable points is the limit

Cantor function

In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is also referred to as the Cantor ternary function, the Lebesgue function, Lebesgue's singular function, the Cantor-Vitali function, the Devil's staircase, the Cantor staircase function, and the Cantor-Lebesgue function. Georg Cantor (1884) introduced the Cantor function and mentioned that Scheeffer pointed out that it was a counterexample to an extension of the fundamental theorem of calculus claimed by Harnack. The Cantor function was discussed and popularized by Scheeffer (1884...

The density of rationals sure do weird things

BAYMAX

Yes,Mystery areas of mathematics.

In the answer you gave link it says we dont even require continuity

of the function

and In your construction the points where sharp edges are there they are countable in number and hence they form a countable set and of whosemeasure is zero@Secret

so incresing functions are differentiable except set of points of measure zero

or increasing functions are differentiable almost everywhere.

So Cantor function is differentiable.

?

A continuous, non-constant, differentiable function whose derivative is zero everywhere except on a set of Lebesgue measure zero.

Secret

well, each bit that is not the cantor set is a horizontal line, thus its derivative is going to be zero everywhere except at the cantor set

The AMS May Eastern Sectional Meeing is aproaching. Various results will be presented

A brief intro on virtual knots

Some samplers for the Mathematical Congress of the Americas 2017

I don't understand what most of these are, except they are pretty

BAYMAX

14:07

Yeah I think they give colour to some meaning , those are pretty :)

Mathematics is pretty :)

I want to save the links for future but I always miss them any idea?

I bookmark a lot i dont want that though

Secret

I don't know if there is a way besides using the chat bookmarking feature or copying all links and put them in some folder

BAYMAX

ok

Secret

BAYMAX

yup nice one

Kasmir Khaan

14:26

Hi chat

how to construct a bipartite graph that is NOT a tree

Simply Beautiful Art

@Secret Nifty

Kasmir Khaan

@SimplyBeautifulArt Hi simply ,how are things with you site and big numbers?

Simply Beautiful Art

@KasmirKhaan Normal? I'm learning how to put weakly inaccessibly cardinals inside ordinal collapsing functions.

Kasmir Khaan

@SimplyBeautifulArt nice i joined your site btw but did not understand how to use it yet =p just chatted a bit

Simply Beautiful Art

lol, okay

Secret

14:29

For Growing functions (I have no interest in finitely large numbers by themselves (no matter how big they are), but I do have interest in anything infinite) : Currently trying to understand BEAF before moving back to ordinal collapse function problem that simple gave me

Kasmir Khaan

@SimplyBeautifulArt do you know graph theory ? =p

Simply Beautiful Art

@KasmirKhaan Who are you though?

Kasmir Khaan

@SimplyBeautifulArt Jack ohara there =p

Simply Beautiful Art

@Secret :P But computable ordinals -> fast growing hierarchy -> large finite numbers

@KasmirKhaan Not really :-(

Kasmir Khaan

@SimplyBeautifulArt well you should learn that when you done with ur big numbers

Simply Beautiful Art

14:31

@KasmirKhaan For what purposes? SCG functions?

Secret

@SimplyBeautifulArt Fast growing hierarchy is ok. I am interested in the recursive properties, levels and limits of the growing functions, more than the actual numbers themselves

Kasmir Khaan

@SimplyBeautifulArt just beautiful subject

Koolman

Is there any moderator

Secret

because these "fixed points" give me a more geometric feeling of these functions and their growth

Simply Beautiful Art

@Secret You can approximate most of BEAF well using FGH

@KasmirKhaan okay

@Koolman They are always watching, even if you don't see them

Paul Plummer

14:32

@Koolman @DanielFischer is one and there is a chat room which moderators hang out in

Koolman

@SimplyBeautifulArt how

Simply Beautiful Art

@Secret You think fixed points are nice? IMO, I am liking how the ordinal collapsing function works :P

@Koolman They read the transcript! :P

Koolman

ohh

Secret

@SimplyBeautifulArt The fixed points give me an idea which growth level (what I previously called Tiers) I am in

The ordinal collapsing function may also help on that, but I still need to understand it

Overall, the limit ordinals are the ones I am most interested, because they are the ones where weird things started to happen

And I like anything weird

Simply Beautiful Art

@Secret Ordinal collapsing functions will allow you to describe fixed points in very compact algebraic formats

Secret

14:37

I also need to learn to stop seeing that $\psi_{\beta}(\alpha)$ thing in the $C_{\beta}(\alpha)_n$ as a veblen function though, cause I realise that's how most of my previous mistakes with the collapsing function arises

Simply Beautiful Art

Hehe

If I may...

$\psi_0(\alpha)=\varepsilon_\alpha;\alpha<\zeta_0$

$\psi_0(\Omega(1+\alpha)+\beta)=\varepsilon_{\zeta_\alpha+\beta}$

$\psi(\Omega^2(1+\alpha_0)+\Omega(1+\alpha_1)+\alpha_2) = \varphi_1(\varphi_2(\varphi_3(\alpha_0)+\alpha_1)+1+\alpha_2)$

A much more compact format:
$\psi_0(0)=\varepsilon_0$
$\psi_0(\Omega)=\varphi_2(0)$
$\psi_0(\Omega^\alpha)=\varphi_{1+\alpha}(0)$

Kasmir Khaan

Construct a connected bipartite graph that is not a tree with vertices {D, E, F, G, H, I, J}

any ideas guys?

Simply Beautiful Art

@Secret It goes further to the multiple argument Veblen function when you take $\psi_0(\Omega^{P(\Omega)})$ where $P$ is a polynomial with exponents less than $\omega$. It easily extends further to the transfinitely many arguments Veblen function as well, and then it leaves the Veblen function altogether.

sdf

Does anyone know what a push-out of a short exact sequence is? Or where I may find a definition of same?

Secret

I see, that's good because the veblen function is so arcane confusing thus I am going to focus on ordinal collapsing

Simply Beautiful Art

14:46

@Secret For the most part, you just need to be comfortable with cantor normal form

Secret

@SimplyBeautifulArt That actually reminds of vectors, imagine those $\omega^{\alpha_i}$ as basis vectors and the coefficients that stick to them as vector components

I am not sure how strong this parallel though

(I am comfortable with anything that look like a matrix, because I think faster vertically than horizontally. This is a reverse of my dream-self)

Simply Beautiful Art

Lol

@Secret then what of $\psi_0(\Omega^{\Omega^\Omega})$?

($\Omega=\omega_1$ for short)

Secret

Uh... actually, I have not read up in detail yet on how to solve for the coefficients in cantor normal form. I only know what it looks like

Simply Beautiful Art

:P

Secret

....If cantor normal form do work like vectors, then the coefficient of $\omega_1^{\omega_1^{\omega_1}}={}^3\omega_1$ has to be 1 and all other terms zero?

Simply Beautiful Art

15:02

What do you mean? I can tell you that is the large veblen ordinal when you put it in the ordinal collapsing function

Secret

For any ordinal $\lambda$ its cantor normal form will look like $\lambda=\omega^{\alpha_1}c_1+\omega^{\alpha_2}c_2 + \cdots +\omega^{\alpha_k}c_k$, and this is what I read so far atm

and $\alpha_i > \alpha_{i+1},\forall i \in \Bbb{N}$

Fawad

If $\dfrac{c^2}{1+m^2}<r^2$ then straight line given by $y=mx+c$ meets circle in how many point?

I think it should be "does not occur or touch circle"

Simply Beautiful Art

@Secret ah, I see what you were saying

Fawad

But it is given it meets the circle in two distinct point.

Secret

So naively, it does look like a vector expansion wrt a basis

Fawad

15:06

Hi @sim @Secret

Simply Beautiful Art

@Secret then what of $\psi_0(\omega_\omega)$? :-)

Secret

$\psi_0(\omega_{\omega})$ is the first element that is not in $C_0(\omega_{\omega})$

$\omega_{\omega}=(I am still reading how to evaluate the $c_i$)$

Simply Beautiful Art

Lol

N3buchadnezzar

Spent a long time writing an answert involving drawing a complex image in latex, 1 upvote. Suvch is life I guess lol :p

Fawad

Nvm it was multiplied by $-$ and sign changed

Simply Beautiful Art

15:17

@N3buchadnezzar lol, yet I do paint in three minutes for trig problems and get upvotes fast if I do it right

N3buchadnezzar

@SimplyBeautifulArt It's art man

Simply Beautiful Art

15:34

:P

TheGreatDuck

hey @SimplyBeautifulArt hows it going?

Simply Beautiful Art

@TheGreatDuck large

TheGreatDuck

i don't get it.

Simply Beautiful Art

Lol, it's okay mate

@TheGreatDuck ...who are you...?

TheGreatDuck

what kind of a question is that?

Simply Beautiful Art

15:38

Hm... Okay rhen

Then*

TheGreatDuck

@SimplyBeautifulArt I want an opinion. If you want to define a multivalued function, would it be appropriate to define it via a solution set or a system of equations?

Simply Beautiful Art

@TheGreatDuck wait, I have a question. How has your study on fractional calculus been?

TheGreatDuck

meh

i kind of gave up on it

Simply Beautiful Art

xD why?

TheGreatDuck

the honors class I was in was going to have us to do this whole mock thesis proposal thing and I was going to do a lot of research, but between that assignment being flat out cancelled due to time constraints for the class and me not having enough time to study frivolous things I gave up on it for now.

Simply Beautiful Art

15:42

Aw, sucks

I feel like giving up on a couple of things right now too

So busy

TheGreatDuck

plus, too many of the functions were unfamiliar so it would pointless for me to try using it for anything. atm, I'm more dedicated to the number theory stuff in the proofing class

Simply Beautiful Art

@TheGreatDuck =P did you solve y = y' ln(y')?

TheGreatDuck

i think it might have something to do with the product integral but i am not too certain of it

Simply Beautiful Art

I actually have no clue what the solution is. Just thought you'd be interested

TheGreatDuck

might not be solvable.

it definitely looks like beyond most methods

Simply Beautiful Art

15:45

Yeah, that's what I thought

TheGreatDuck

laplace transform might work partially but it would end up hitting a roadblock when solving for Y(s)

i hate lalplace transform with a fervor

at least, when it is used egregiously for trivial things like step functions

Simply Beautiful Art

Lol

That's how you roll

TheGreatDuck

well I'm also a CS major

Simply Beautiful Art

*coughs because I can't even*

TheGreatDuck

efficiency is absolute

Secret

15:47

@SimplyBeautifulArt. Actually, I have a question about the fast growing hierarchy. Why define e.g. $f_{\omega}(n)=f_{\omega [n]}(n)$

We knew that $f_k(n)=f_{k-1}^n(n)$

Now since $\omega=sup(\{0,1,2,3,\dots\})$
Then naively $f_{\omega}(n)=sup(\{f_0^n(n),f_1^n(n),f_2^n(n),\dots\})$

Why choose the nth term of this sequence?

Simply Beautiful Art

I can imagine @TheGreatDuck

@Secret simplicity

TheGreatDuck

@SimplyBeautifulArt granted, there is also case inefficiency (I made up that term) where the sheer number of different cases to handle in and of itself produces inefficiency.

Simply Beautiful Art

Mhm

TheGreatDuck

you ever do programming?

Simply Beautiful Art

Only with the size of outputs in consideration

Almost contrary to efficiency

TheGreatDuck

15:54

efficiency is memory and speed

Simply Beautiful Art

Mhm...my programs basically need infinite memory and time

@TheGreatDuck say, did you get on Discord?

Secret

Uh...
$\omega_1=\sup (\textrm{all countable, i.e. all expressions of $\omega$})$
$\omega_2 =\sup (\textrm{all expressions of $\omega_1$})$
$\omega_n=\sup (\textrm{all expressions of $\omega_{n-1}$})$

None of these are expressible in terms of any ordinals lower than itself,. In addition, they are all epsilon numbers, thus their cantor normal form: $\omega_{\alpha}=\omega^{\omega_{\alpha}}$ i.e. itself

Simply Beautiful Art

@TheGreatDuck efficiency for me is the size of my program

@Secret mhm?

TheGreatDuck

@SimplyBeautifulArt no i haven't gotten on discord. Is that the chat you were referring to back on puzzling?

@robjohn hello. How's it going?

Transcript for

$Mathematics$ Mathematics