Mathematics - 2015-10-20 (page 1 of 2)

anon

00:00

he's trying to show there is a category whose objects are natural numbers in which hom(n,m) is the set of nxm matrices (over an unspecified field...)

in particular, he checks the maps hom(a,b)xhom(b,c)->hom(a,c) are "associative"

his command of english is a bit off but yeah

actually, I think he should make hom(m,n) the nxm matrices (notice m,n in a different order)

user105491

@anon I'm confused. How does one compose hom-sets?

anon

it's essentially equivalent to the subcategory of Vect whose objects are F^n for each n

@SanathDevalapurkar do you know the definition of a category?

user105491

@anon Yes.

anon

you have to be able to compose morphisms together

that's part of the definition

user105491

One can compose elements of hom-sets

user105491

00:04

not hom-sets themselves

anon

I said the map hom(a,b)xhom(b,c)->hom(a,c)

user105491

Right, right. I'm talking about the post itself.

anon

composition is the map that I just said

composition takes as input two morphisms, and outputs another morphism

user105491

I understand that; but the post talks about composing whole hom-sets themselves

user105491

see the second paragraph

user105491

00:05

(Also, you can't compose elements of hom(a,b) with elements of hom(c,d), although that's what I understand is the operation being done somewhere in the post)

robjohn

@AntonioVargas Pretty well. I wasn't really calling, I just dropped in and saw that the population was down.

@AntonioVargas how are you?

anon

@SanathDevalapurkar Like I said, I believe he's trying to show associativity of composition (based on the assumption of associativity of matrix multiplication). whether he knows how to use english correctly is a different story.

user105491

Sure.

anon

also, his symbolic derivation makes no sense to me either

user105491

That was my main confusion when I read the post linked to by @Josh

Antonio Vargas

00:08

@robjohn Not too bad. Just seeing if there are any good questions to look at.

morphic

Wow it's Sanath..one of my math heroes

user105491

@morphic Are you being sarcastic? (My apologies if you're not, an electronic format is not the best way to judge emotions)

morphic

@SanathDevalapurkar No

Sometimes I tell people at my school about people I know from here and they didn't believe you were a real person lol

user105491

Thanks for the kind words!

morphic

Sanath one of the PhD candidates at my school wanted to do stable homotopy theory but professors were discouraging him saying it was too difficult, and that the professors themselves attempted research in it and failed so it's too hard for the student to pursue

user105491

00:22

I don't think that's right.

user105491

If the student wants to learn stable homotopy theory, then he should do it, regardless of whether a professor failed in it or not

morphic

Well I guess he needs an advisor first, at least in name

user105491

Sure, I get that

user105491

Although if he wants to pursue it for his own sake, I'd encourage him to do so

user105491

It's a very welcoming field, and everyone who I've met/talked to is really nice.

user105491

00:24

I'm sure he's seen this question already: mathoverflow.net/questions/149021/…

user105491

It's pretty helpful

user105491

@morphic Are you an undergraduate?

morphic

@SanathDevalapurkar Yes

user105491

Cool

user105491

Anyway, I have to leave

user105491

00:27

Great chatting with you!

morphic

Ok, have a good evening

user105491

You too!

Jeff

00:49

Is there a symbol for subspace (sub vector space) like $\subset$ is a symbol for subset?

anon

just use subset symbol and say subspace

Jeff

Do you put "subspace" after the superset? $W \subset V$ subspace?

anon

"let $W\subset V$ be a subspace", "consider the subspace $W\subset V$ defined by..."

Jeff

k. ty

user143442

are there famous gay mathematicians besides Alan Turing?

morphic

01:07

There's one in this chat

user143442

@morphic who?

Julian Rachman

Hey everyone.

@anon in regards to my blog post: I appreciate the clarification of my post. I will try to fix the things you mentioned above later today but if you could, could you leave it as a comment on my blog so that I can see where I went wrong after the fact?

In addition, my English is not bad. I just can't properly express my thoughts and answers in a clear way yet.

@Josh lol I don't think many people just "run across me." That shouldn't happen haha.

Semiclassical

01:47

@AntonioVargas just saw your name mentioned here, thought i'd say hi

Antonio Vargas

02:16

@Semiclassical hey man, how are ya?

Semiclassical

eh

Antonio Vargas

me too

Semiclassical

not great. went back to being a TA this semester, for the first time in two years

and while i've been able to pick up the student interactions just fine, grading...not so much

Antonio Vargas

yeah, bummer

Semiclassical

by which i mean "i've been so late on two big grading assignments that i've gotten the profs attention"

Antonio Vargas

02:18

you've told me how much grading there is for the TA

oh lol

Semiclassical

honestly, it's not so much the amount of grading.

i used to be able to get through it

but my anxiety about it has gotten far far more acute than it used to be

Antonio Vargas

that's rough

I can kinda relate

I didn't take a TA position this semester because of some similar reasons

Semiclassical

i wish i hadn't now. i mostly did it so that i could draw a paycheck again

and health insurance, etc.

but at this point i'm basically a liability from a course perspective. being able to coordinate labs/discussions/tutoring is an important part of being a TA, but so is grading...

Antonio Vargas

yeah, there isn't really a choice a lot of the time

Semiclassical

tbh, i'm back to "i need to get the hell out of here" logic

Antonio Vargas

02:22

Do you daydream about the heights you could achieve outside academia?

I do

Semiclassical

eh. i more daydream about having a career that's not crazy-making

Antonio Vargas

It's a nuthouse. But in reality I'll still try to make it work.

Semiclassical

in the short term, perhaps i will. long-term? academia can go away

for me, i mean

Antonio Vargas

Do you think you'll leave after the PhD?

Karim Mansour

@anon sorry about yesterday with that topology question was stupid the reason but yeah your reasoning is 100 % correct my mind yesterday was just sick to fill in the details. The problem again if some people want to learn from it is Suppose X is a topological space with finite complement topology. Consider arbitrarily x \in X and arbitrarily punctured nbhd $U_x$ of x. Since $U_x$ is open hence $X - U_x$ is finite, since $A - {x}$ is infinite so it is not subset of that.

Semiclassical

02:25

quite certaintly

hell, i'm not sure about sticking out the phd. haven't been for a while, and this hasn't helped

Karim Mansour

so that means that there exists element u $\in A - {x}$ such that u $\in U_x$

Antonio Vargas

In that case I'm happy for you :)

Semiclassical

hah.

Karim Mansour

your not gonna continue in academia @Semiclassical????

whyyy

Antonio Vargas

I don't know if it's just a sunk cost fallacy, but I feel like I've put way too much into the program to stop before the degree.

I want the letters after my name at least

Semiclassical

02:27

because academia is an inherently crazy-making institution?

the phd for me is pretty irrelevant. (i'll definitely leave with an MS in Physics---no way i'd leave that on the table)

i really don't know what i want as far as a career path, though

i just know enough about what being in academia as a grad student has done to my head that the idea of doing it for the rest of my life makes me shudder in horror

Antonio Vargas

heh

Semiclassical

sad thing is, i actually do like research conversations.

Antonio Vargas

Yeah, definitely

Semiclassical

but as i think i've said before, research as teaching/learning != research as profession

same thing with education itself, really

though honestly if my anxiety wasn't so bad when it comes to such things i could probably cope. (note that i say cope, not thrive).

speaking of research stuff, how much do you know about kernels? (e.g. Christoffel-Darboux for orthogonal polynomials) @AntonioVargas

Antonio Vargas

Not much actually. I've fallen behind on my OP studies.

Why do you ask @Semiclassical?

Semiclassical

02:35

just curious. had been doing some reading on them, especially re: asymptotics

Antonio Vargas

Are they connected to the RH formulation?

Semiclassical

i think so? it definitely seems like it. let me find the main paper i know

Here's a review paper on CD kernels in OPs: ma.utexas.edu/mp_arc/c/08/08-107.pdf

RH is only mentioned as an aside, but it's a rather intriguing aside

Antonio Vargas

Yeah, let me check out the Kuijlaars, Vanlessen paper

gotta fire up the vpn...

Semiclassical

think you may have pointed it or one like it to me, actually

Antonio Vargas

I have too many to keep track

Semiclassical

02:40

gotcha

the paper of Lubinsky mentioned is this one

Antonio Vargas

Wow it's short!

Semiclassical

which, Lubinsky or KV?

Antonio Vargas

Lubinsky's

Semiclassical

ahh

Antonio Vargas

I think I'll dedicate tomorrow to seeing what I can get from these

Semiclassical

02:43

neat

Antonio Vargas

Oh btw @Semiclassical, in an act of desperate procrastination I wrote a little userscript to display a live preview when writing comments on Math SE. Want to see?

Semiclassical

oh-hoh, sure

Antonio Vargas

Here's the meta post

Semiclassical

ahh. i don't have tampermonkey, but i'll see if i can check it out eventually

Antonio Vargas

It was pretty fun, the writing process.

I like programming. Learning it is easier than learning math.

Semiclassical

02:52

depends on the math, sometimes

but then, certain kinds of math are more like programming than others.

and some are more like obscure russian literature or german idealist philosophy

Antonio Vargas

^ my life

Semiclassical

i'm perfectly happy to read people talking about the last two, but i'd rather not read them myself

dafinguzman

03:12

Hello everyone

Antonio Vargas

Hi @dafinguzman

dafinguzman

I have a question. Wandering around I found this post math.stackexchange.com/questions/991989/…

and wondered why it didn't have any answers

I made a search and found many related questions

Antonio Vargas

Maybe no one found it interesting enough to answer. Apparently you didn't even find it interesting enough to upvote it :)

dafinguzman

In particular, this and this post have answers that I think answer the first question

Should I mark it as duplicate of any of them?

Antonio Vargas

I can't say. I don't have a good enough foundation in functional analysis to judge. It couldn't hurt though- the worst that can happen is that people in the review queue won't agree with your vote.

dafinguzman

03:19

ooh, I see

I've never marked a Duplicate before, it's kind of scary the first time

good to know it will be reviewed. thanks!

Antonio Vargas

Oh yeah, nothing to worry about @dafinguzman :)

Anthony

04:20

@TedShifrin Ribet said he'd write me a letter, but he seems to think it would be better to get it from my post doc. In general he's nice, but in addition I think I've established a decent correspondence with him so I'm tempted to see if I should try get him instead- but currently I'm thinking the post-doc knows me better, and might write a more compelling letter. We'll see.

Karim Mansour

are you postdoc @Anthony?

Anthony

@KarimMansour Naw I'm an undergrad

@KarimMansour Are you an undergrad?

Karim Mansour

yes

Anthony

Yeeeeeeehhhh

Miguel Román

Hello! Can someone help me with a very basic and fast thing =D?

About the antidual space

Antonio Vargas

04:36

"Just ask; don't ask to ask."

Miguel Román

04:51

Let $V$ is a vector space of finite dimension over the complex numbers and let V^# be the antidual space i.e the space of maps h:V \to C such that h is antilineal. I want to prove that there's a natural identificacion of $V$ with the double antidual space (V^#)^#.

I think that this is similar to the dual space sending a to the evaluation of a. But this map is not antilineal. Maybe some modification of this idea

anon

05:16

maybe postcompose evaluation with conjugation to get the map V->(V^#)^# ?

Ted Shifrin

05:38

With two antilinears, aren't we back to linear?

@Anthony: I thought you had already convinced me. If you were going pure math, Ribet would be a strong preference. But you're not.

Karim Mansour

@TedShifrin hi

Huy

06:06

@TedShifrin: I think I was just thinking too complicated. I just computed the Jacobian of a Möbius transformation and now it's obvious

Ted Shifrin

Ok @Huy :)

Rehi @Karim

Karim Mansour

just solving some field and ring theory questions

did you teach ring theory @TedShifrin when you taught algebra ?

or was it only groups ?

Ted Shifrin

In my course rings was first semester, groups second.

Karim Mansour

it actually makes sense to do it that way

Anthony

@TedShifrin Sure, sure.

Ted Shifrin

06:14

It's not the Bourbaki way, but it's more pedagogical and historical @Karim.

Anthony

Uh I think I forgot the Fundamental theorem of calc

whoops

Ted Shifrin

Spanks Anthony

Karim Mansour

I see

our complex analysis prof mentioned bourbaki

that is they wanted to make math super rigorous

Anthony

How do I evaluate $\frac{dh}{dx}(1)$, where $h(x) = \int_0^{x^2}e^{x+t}dt$ ? I know I can compute it directly, but is there a way of doing this with the fund theorem?

I'm confused because the antiderivative would be with respect to $t$, and then I'm taking the derivative of $h$ with respect to x.

Karim Mansour

I agree actually with bourbaki group but not when you starting math

did you ever read the books by them ?

@TedShifrin

Ted Shifrin

06:17

Put a $u$ in the limit. You'll need to use chain rule, FTC, AND diff under the integral. Studying for GRE?

Anthony

:P

Differentiation under the integral!?! I never learned that! Feynman cites it.

Ted Shifrin

A little, @Karim. Not my style for math.

Anthony

And yeah, studying for the GRE.

Ted Shifrin

Google, @Anthony

Anthony

Yeah, I was just saying. I have a tab open.

Ted Shifrin

06:20

I don't want to spank twice. :)

Anthony

Oh, well this is exactly what I have.

I assume that we were meant to integrate directly in this problem.

Gigili

Hi

Ted Shifrin

I don't.

Gigili

What is efficiency in mathematical context?

user685252

Hi

Anthony

06:21

Really? Is differentiation under the integral standard? Ugh.

Ted Shifrin

Yes. It's everywhere in applications and grad stuff.

It's an exercise in a good advanced calc course.

Gigili

@anon

Tobias Kildetoft

@Gigili Could you provide a bit more context?

Ted Shifrin

Good morning @Tobias

Gigili

In the introduction of a paper, first it is asked if the problem is well imposed, then it is asked whether it can be solved efficiently

Tobias Kildetoft

06:24

@TedShifrin 'morning (or I suppose late evening where you are)

Gigili

Signal processing and dictionary learning

Mike Miller

If there were any questions about differentiating under the integral sign when I took the GRE I got them wrong.

Ted Shifrin

Oh, Balarka will be sorry to have missed you, Mike.

Karim Mansour

I forgot most of that stuff haha

Ted Shifrin

At your age, you shouldn't forget stuff, Karim.

Gigili

06:27

Please answer my question when you have time, @anon... Thank you

Anthony

@TedShifrin I feel like just applying the differentiation under the integral is enough.

Karim Mansour

yeah but if I review it I guess I would remember them

Ted Shifrin

Poor anon is expected to know everything,

Anthony

I assume anon knows everything.

Ted Shifrin

No, Anthony. The FTC comes in too.

Anthony

06:31

Hmmm. Don't we have $\frac{d}{dx} \int^{x^2}_0 e^{x+t}dt = 2xe^{x+x^2}+\int^{x^2}_0e^{x+t}dt$?

By the diff under the integral?

Ted Shifrin

You used FTC for the first term, @Anthony.

Anthony

Oh, did I? I just took the formula from Wiki. :P

Anyway, thanks @TedShifrin.

Balarka Sen

07:15

@SanathDevalapurkar That's kind of an unnecessary pedantisism, to be honest, haha. It's clear what he meant.

Jake

I'm looking for the name of something I'm pretty sure should have a name. Say I want to integrate over a vector valued function until a certain threshold in magnitude is reached. That is the "intergal" of the sort I am looking for has this property: if the intergal of F from a to b is x and |x| > threshold then the intergal from a to c where c > b is also x.

That is, after a certain threshold is met it doesn't matter how much further you integrate, it will just be what ever vector it was when the threshold was met.

Does this sort of thing have a name?

Tobias Kildetoft

07:39

Wow, what a nice and detailed abstract arxiv.org/abs/1510.05080 :)

Balarka Sen

hahah

Chris's sis the artist

08:58

@robjohn Hey! I was wondering if Mathematica 10 can do anything about $$\int _0^1\int _0^1\log \left(x^2 y+x y+x+y^2\right) \ dx \ dy$$

It's a resistant integral, my Mathematica fails do calculate it.

It's interesting the pattern inside

$y-y-y^2$

$x-x-x^2$

They come together with step delayed. Well, this is just an observation, not sure if it has a certain significance in the calculation of the integral.

robjohn

10:08

@Chris'ssistheartist I will try when I go to that computer. The argument to log looks very ugly.

Chris's sis the artist

@robjohn OK. Yes, it's not nice at all. :-)

Gennaro Marco Devincenzis

12:14

anybody knows this differential equation? $$-y''+2xy'+(1+2x^4-2\alpha)y=0$$

2

robjohn

@Chris'ssistheartist It converts it to a very nasty looking single integral.

Chris's sis the artist

@robjohn Yes, I know. Maybe there is a way to avoid that.

robjohn

@Chris'ssistheartist I don't know how... I assume you have a closed form?

Chris's sis the artist

@robjohn I'm working on it yet.

Huy

12:51

@DanielFischer: BTW, I think I understand now what my prof meant the other day. We want to define some sort of $H^1$ norm on the upper half plane which is invariant under isometry. For the function itself, we'll take the hyperbolic norm, whereas for its derivative we'll have to take the Euclidean one to guarantee invariance. I haven't checked it yet though, but I think that's what he meant.

Daniel Fischer

13:07

It would be a funny way to express that. Well, differential geometers speak a different language.

user105491

@BalarkaSen The notation confused me because I wasn't able to figure out whether the post was doing something new or if it was telling us about a known category.

Huy

@DanielFischer: What do you mean by that? :D

Balarka Sen

13:29

@SanathDevalapurkar Fair enough.

Tien-Cheng Huang

13:44

Could someone explain the historical motivations of the concepts of Banach space and Hilbert space? (Reddit r/math Simple Questions redd.it/3p0626)

barznjy

14:28

hi

Huy

Hilbert space

The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used. Hilbert spaces arise naturally and frequently...

barznjy

I have a question

Krijn

Just ask; don't ask to ask

barznjy

why some people give down-vote to the question without telling reason?

Krijn

People tend to be unreasonable

Its sad, but you can't really do anything about it

barznjy

14:39

I think there is no stupid question, the stupid is the person who think its stupid

Krijn

That is true

MickLH

@GennaroMarcoDevincenzis Is $2\,x^4+x^2-2\,\alpha+1$ positive, negative or zero?

Krijn

However there are people that post homework questions without doing any thinking themselves, which should be downvoted and explained

barznjy

I agree with you. But in all cases you should give feedback to the questioner so that he know his weak points

anon

@Gigili it might be related to computational complexity (how much time and space resources we expect an algorithm to utilize in the worst-case scenario as a function of the input's size)

sorry I wasn't around earlier

Gigili

14:50

@anon Yes, that probably is what the author is talking about. Thank you =)

N3buchadnezzar

heya

Galois in the Field

15:23

ayeh

Tien-Cheng Huang

15:37

@Huy In fact now I think taking a read about "Banach space" and "Hilbert space" from "The Princeton Companion of Mathematics" would be more appealing than reading Wikipedia's articles.

The Princeton Companion to Mathematics*

Krijn

Why $\frac{\cos^{-1}(\frac{1}{5})}{\pi} \notin \mathbb{Q}$?

konewka

Don't know

Balarka Sen

@Krijn niven's theorem.

if $\cos^{-1}(1/5)/\pi = \theta \in \Bbb Q$, then $\cos(\theta \pi) = 1/5$. impossible, by niven's theorem.

konewka

15:52

Fair enough

Krijn

Does this not only imply that $\theta \pi \notin Q$, or am I missing something

(and therefore that $\cos^{-1}(1/5) \notin \mathbb{Q}$)

konewka

As $\theta$ is in $\Bbb Q$, $\theta \pi$ would indeed not be in $\Bbb Q$

Krijn

So it does not prove that $\theta \notin \mathbb{Q}$

konewka

$\theta$ is in $\Bbb Q$ by assumption

Balarka Sen

No, you're both misinterpreting Niven's theorem.

It says cos of a rational multiple of $\pi$ is rational iff sin of that thing is $0, \pm 1,\pm 1/2$

Krijn

15:57

$\cos(\theta \pi) = 1/5$ implies $\theta \pi \notin \mathbb{Q}$

Balarka Sen

$\theta \pi$ is a rational multiple of $\pi$.

Krijn

Ah, yeah

The wikipedia page should be updated :D

MickLH

16:34

Update it.

evinda

Hello :)

MickLH

:)

evinda

How are you? @MickLH

MickLH

I'm doing well, I've spent all night doing audio engineering and the sun crept up on me.

evinda

Aha @MickLH

MickLH

16:37

But I now have a mistakably similar instrumental for this song: soundcloud.com/buygore/forbes

MickLH

16:47

(And that is on topic! I had to use Mathematica to help me with some nasty integrals so I could get some of the sound effects perfect)

evinda

Interesting @MickLH

GBeau

17:38

When solving a bunch of problems yesterday morning in my analysis text, it occurred to me after a while on this problem that it's not true when I came up with a counter-example. I pointed out the error to the author and he noted it for the next revision, but what do you think is a good additional assumption to patch the conclusion?

Daniel Fischer

@GBeau It's true if you use the definition of $\lim\limits_{x\to c_1} f(x)$ that doesn't exclude $c_1$ from the admissible values of $x$ (unless $c_1$ is not in the domain of $f$). [Here, the pertinent point is $c_2$, and the relevant function is $g$.]

Agawa001

its crazy rainy in this place

Daniel Fischer

Monsoon?

Agawa001

yes sahel monsoon

GBeau

@DanielFischer my counter-example was $f(x)=c_2$ around some neighborhood of $c_1$, then trailing up to the right and down to the left outside of that (to ensure it clusters). Then, just leave $g(y)$ undefined at $c_2$ or with a point discontinuity such that the limit is $L$ but $g(c_2)\neq L$. Since $f(x)$ is constant at $c_2$ around the neighborhood of $c_1$, the limit of $h(x)$ becomes exactly $g(c_2)$

although I thought I understood what you meant by not excluding the $c_1$, I'm not sure it fixes the example

although I guess if you require the same for $g(y)$ it works!

Daniel Fischer

17:54

@GBeau $f$ is assumed to take values in $B$, the domain of $g$. So you can't leave $g(c_2)$ undefined.

GBeau

@DanielFischer ah! but the point discontinuity works? (that's what I used in the email to the author, since I was most certain about the domain requirements)

Daniel Fischer

@GBeau Yes, as [I said], $g$ and $c_2$ are the things that count here.

GBeau

all right :)

Daniel Fischer

@GBeau Yes, if you use the definition of limit that excludes the "critical" point, then the discontinuity example works.

GBeau

that's a good point about requiring it to be defined there, it hadn't occurred to me (I had merely made my counter-example to the author where $A=B=\mathbb{R}$ out of simplicity for obviously satisfying any clustering requirement)

We can just require $g(c_2)=L$ and use the book limit (doesn't include the point) as well I think?

and I'm not sure how hard it would be to prove, but would think merely requiring $f(x)\neq c_2$ in some neighborhood of $c_1$ (not including $c_1$) also works

Daniel Fischer

18:03

@GBeau You mean $g(c_2) \neq L$, methinks.

GBeau

@DanielFischer I meant as an additional condition to the problem for it to be true

Chris's sis the artist

@Agawa001 After some homeopathic remedies my condition improved a lot, at least so far. Tons of other traditional medicines failed.

(human beings are also designed in a spiritual dimension, that's why)

Agawa001

@Chris'ssistheartist homeopathic remedies ?

Chris's sis the artist

@Agawa001 Yeah.

Agawa001

plz excuse my lack of knowkedge what do you mean ?

Chris's sis the artist

18:12

Homeopathy

Homeopathy (/ˌhoʊmiˈɒpəθi/) is a system of alternative medicine created in 1796 by Samuel Hahnemann based on his doctrine of like cures like (similia similibus curentur), a claim that a substance that causes the symptoms of a disease in healthy people would cure similar symptoms in sick people. Large-scale studies have found homeopathic preparations to be no more effective than a placebo, suggesting that positive feelings after taking homeopathic medicines are due to the placebo effect and normal recovery from illness. Homeopathy is a pseudoscience—a belief that is incorrectly presented as scientific...

The description on wikipedia is not good enough for me.

Agawa001

yes, too long, cant get its tail from its head

Chris's sis the artist

I don't care at all what they actually say on wikipedia, I only know I feel far far better than before. No placebo effect since I didn't trust the way at the beginning.

anon

reminds me of the show where derren brown set out to convert an atheist.

Mary Star

Hello!! Could someone of you expain to me how we conclude from $\cos^6(t) = \cos^6(s)$ that $s = \pi - t$ in $[0,\pi]$ ?

anon

you can conclude $s=t$ or $s=\pi-t$ no?

$x^6=y^6$ implies $x=\pm y$ when $x,y\in[-1,1]$. the equality $\cos t=\cos s$ implies $t=s$, and $\cos t=-\cos s$ implies $s=\pi -t$. (assuming $s,t\in[0,\pi]$.)

Mary Star

18:27

Oh I see... Thanks a lot!! :-) @anon

Tien-Cheng Huang

Which abstract algebra textbook is most frequently used for preparing math PhD prelims in the U.S.?

Chris's sis the artist

Yeah, but what is the greatest irony? The irony to believe you're the real one (as you make fun of God), and actually to be wrong, because if God exists he is present on the whole time axis while you, as a human being, taking into account the infinity of the axis you can simply say you don't even exist.

Anyway.

Let me put again my lastest integral here

$$\int _0^1\int _0^1\log \left(x^2 y+x y+x+y^2\right) \ dx \ dy$$

Agawa001

@anon atheism isnt a religion to be converted from

anon

I never intimated otherwise. Derren set out to convert a nonbeliever into a believer.

(social movements usually have many things in common with religions though, which is why many see movement atheism, e.g. New Atheism or whatever, as a kind of religion)

Chris's sis the artist

18:45

@Agawa001 The thing that I don't understand at the major part of the atheists I know is that they speak about God more than believers do (yeah, it's like a religion to them). For me it's simple, if I stop believing in God, I don't spend time talking about something that doesn't exist, because it simply makes no no sense, it's a loss of time at best.

Agawa001

@Chris'ssistheartist some kind of agnostics, struggle to find god while they dont believe he exists

something is absent until proven existent

i knew someone in real life like that, he wasted lot of time finding goddess where he s supposed to find and build himself

anon

@Chris'ssistheartist I think many atheists devote more time to thinking about religious beliefs, such as Yahweh of the Bible or deistic versions of supreme beings, than other harder-to-analyze political and moral topics because philosophically it is a very broad and prototypical thought experiment, not to mention fun and engaging.

one can look at it from many angles and form many opinions and deductions based solely on common knowledge and experience, as opposed to looking up statistics on this or that or histories and economic theories etc. in politics which require a lot of research and training (if one wants to do it right).

On the other hand, religious belief is a rather core fundamental disagreement atheists have with believers which a vast number of other disagreements on political, moral, intellectual, psychological, spiritual etc. beliefs all over the spectrum can be traced back to, so of course it makes sense they will devote time to the underlying root of the problem (as they see it).

Agawa001

i was speaking about massive vaccination and they called me a troll for it, lets not go so far in theology

anon

it's one thing to say atheists are wrong or not open-minded, but saying they're wasting their time even according to their own worldview is what I think doesn't make sense

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$Mathematics$ Mathematics