@anon In my opinion they do it because they need support for their belief, so talking every day about it, arguing with the believers they try to obtain more credit for their religion that is the atheism. Also considering the religion at being the root of all bad things in the world is one of the things they debate about every day, but of course, this is nothing than staying in an extreme corner and reducing everything to a simple cause of evilness, that is the religion.

Maybe it's a genetical matter to talk about God ceaselessly, also some study showed that many atheists are angry with God, but no matter the reason, I cannot understand the attitude of talking about something that doesn't exist all day long and then pretending to be rational. Mathematically speaking, how could I blame the religion for everything that happen in the world?

What is the probability to say that all bad thing that ever happened to you were because of the religion? I think you see my point.

If I was an atheist, I'd really see no point in spending time arguing with the believers. The problem is that the existence of God is not a religion.

religion is cool until its about killing and abusing others rights. dot.

There are tons of religions out there? OK, I see that. I'm only interested in the truth.

@Chris'ssistheartist they are enumerated not weighted :D

@Agawa001 :D

Hello! Would someone like to explain what is "mathematical maturity"?

@Tien-ChengHuang It is a vague term referring to how long one has been exposed to mathematics of a certain level

I wish to hear some top mathematicians explaining what is "mathematical maturity" and how to cultivate it in their viewpoints.

I don't believe that "mathematical maturity" just means ability to understand terse textbooks or tackle in-class exams.

@DanielFischer: do you know how to find a best fit distribution for a given set of data?

@Chris'ssistheartist the "they do it for self-assurance" seems very armchairy and convenient. the "religion is not the root of all evil" opinion I agree with. but faith and dogma, historically and currently very important components in organized religion, I think are a big part of it.

much of the good of religion can be divorced from faith and dogma and myths I think, even if some believers don't think so. the "many of them are angry at God" sounds like you're falling into Poe's law (unintended self-parody difficult to distinguish from making fun of believers). I am sure the newly-converted wish there God was real so they could be angry at.

others are hyperbolic against the God of the Bible as a rhetorical strategy, to emphasize his not being a role model for good behavior or not conforming to the benevolent figure many understand him to be, or else to push others to be objective in their appraisals of him.

many of atheists really are angry at believers for hoodwinking them all their life - being a devout believer often requires so much commitment and trust that their anger for being taken for a ride I think should be understandable.

there is also the part where other believers will make up just-so stories and narratives for why and how an atheist stopped believing, or otherwise gaslighting or manipulating them, which is another reason ex-theists can be jaded. your "say all bad things that ever happened to you were because of religion" seems as much a strawman as "talking about something that doesn't exist all day long" - surely they do other things during their day.

but I've already told you why there are numerous atheists - activists and bloggers and so on - that talk about it so much - because it's interesting, because it may have actually affected their lives deeply (ex-fundamentalists), or affected friends and family they care about, or is adversarial to things they care about

(liberals and abortion, contraception, homosexuality / scientists with evolution, stem cell research, climate change), or because they think it is the root of many important disagreements in all sorts of arenas - politics, morality, spirituality, psychology, science, etc.

to say it's a waste of their time to talk about religion (of which Yahweh of the Bible is just one small but critical part) is about as sensible as saying everyone is wasting their time talking to anyone else about anything at all they disagree with. answering all of these objections is well-covered territory. if these questions interest you, you can find some atheist writings to read or find atheists to talk to.

sorry, didn't mean to take up the whole screen

I'll use pastebin next time

@anon boy, you have spent some serious time thinking about this.

awed

I stopped believing 10 years ago, and my mother is a fundamentalist.

@Huy Not really. Don't you just try to fit various models to your data and look which you find cutest?

In fact... I just sent an e-mail to Terence Tao requesting him to clarify the meaning of "mathematical maturity" and how to cultivate it in his viewpoints on his blog.

@anon ah.

I never really cared much about existence/non-existence of God. I am a neutral person.

:P

@DanielFischer: That's what I thought but surely there must be a better way to do it.

I mean, it's not possible to logically derive or refute existence or non-existence of God with the amount of logical faculty I have, so what's the point?

@Huy I'm sure a statistician can tell you more about it. And explain some good criteria for what shall be considered a better fit than something else. But I've long forgotten about it.

@BalarkaSen it's not possible to logically derive or refute any decision or course of action in the real world, or even disprove the universe was created Last Thursday with our memories elaborate fabirations. but we still act and make choices in the world.

What's a real world?

plus, nobody takes that attitude towards e.g. Zeus (common talking point, except usually with Santa)

I vaguely remembering hearing about it, but I don't know what it is. :D

@anon hmm?

anyway, I have to go

yeah, bubye.

@Chris'ssistheartist surprisingly, wolfram spit out an answer for a partial (riemann) summation of the first integral in terms of gamma functions

I had to add extra terms that go to zero in the limit, though

@GBeau Interesting. I cannot do much with W|A these days, without an account.

I'm downloading my university-provided copy of mathematica since that was about the best it could do

@Chris'ssistheartist where this needs multiplied by (1/n) and then the limit as n->infinity to get to the first integral (here, kl=y)

@GBeau That one looks scary ... :-)

if l=1/m, it's the same sum again over k to m-1 for the next integral

so that's why I started downloading mathematics :P

mathematica*

@anon i havent made that risky choice of refuting all the goddess, but i can choose to refute what i dislike about religion, like inequality between genders and holy war etc

i still believe in god and he wouldnt be pissed off so much of me refusing these illogical notations in my religion

@Chris'ssistheartist the placebo effect healed my cardiac issues, old people told me that its evil spirits but it takes me to jog everyday 1 km long atleast to regain my heart-beating equilibrum

and i dont think the meds did too much

@Agawa001 I see.

@Agawa001 I also go jogging almost every day (well, with some exceptions since I have experienced difficulties with allergy).

I'm happy I don't cough anymore and I can work silently.

i also practise meditation to repulse off lifestyle diseases as much as possible since this village is a case of urbanisation and we wont enjoy the nature anymore

@anon Here I'm aware of some that launched an atheistic champaign and spread all kind of stuff about Christians saying they are retarded, low IQ profile, uneducted, and what not. I mean I'm very kind to call that just "a waste of time", not more, since it can be called differently, and maybe depending on the area where you live, things might look differently, but here I noticed what I described above. Religion is a sensitive topic,

it was like that, and it will be like that, and the fact that someone is deeply affected by religion doesn't mean that one has the right to label people as above. In fact, the smartest people I met so far were Christians, that is just my experience, of course, and I don't pretent that you all should have the same experience.

And I'm not falling into any Poe's law, that was a study that can be found on internet, and, of course, if one is a real atheist, I mean not one full of doubts, claiming all day long that there is no God, and that at the first difficulty says "God save me!", then it's perfect. You know, I'd really be curious to meet atheists that have absolutely no doubts about their religion.

people of the city want to come here and contaminate us with their modern civilisation diseases

i enjoy the nature, i love the forest, the mother ground, the wood, but i dont think it would be an option anymore

(+1) Star! :-)

@Chris'ssistheartist do you like the nature ?

@Agawa001 I'm surrounded my nature! :-)))) I live in the countryside too.

@Chris'ssistheartist so take profit of each second, the nature wont remain as humans insist of concreting it everywhere

@Agawa001 Yeah, I'm aware of it.

@Chris'ssistheartist I realized I had never asked mathematica to try the integral directly - it was only able to reduce it to a single integral: $$\int_0^1 \frac{1}{2} \left(2 \left(x^2+x+2\right) \log (x+1)+2 \sqrt{-x \left(x (x+1)^2-4\right)} \left(\tan ^{-1}\left(\frac{x^2+x+2}{\sqrt{-x \left(x (x+1)^2-4\right)}}\right)-\tan ^{-1}\left(\frac{x (x+1)}{\sqrt{-x \left(x (x+1)^2-4\right)}}\right)\right)-x (x+1) \log (x)-4\right) \, dx$$

"reduce"

@GBeau which one ?

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

I'm dumb so I don't know all Chris's fancy integration tricks so I was just playing around with the definition

how the hell did mathematica do that

@GBeau Yeah, but from that point there is still a long way to go, at least it seems so.

Anyway, I just realized tomorrow I'll have a lot of non-mathematical work to do, so I won't work on my book at all, no research, but maybe during some breaks I'll manage to think of some of my latest research.

I have many ideas that have been waiting for me to develop them, but that means time, more time, more more time ...

The amazing thing in mathematics (and I say it again and again since it's lovely to say it) you start from a simple result and then realize you can write a whole book after developing things enough.

Also this integral doesn't come out of blue, that is $$\int _0^1\int _0^1\log \left(x^2 y+x y+x+y^2\right) \ dx \ dy$$ but you do research, and research and again research, and then the results push you toward it.

I got a prob

toss it !

Gotta prove that infA for $A=\{\frac{1}{n}|n\in \Bbb N\}$ is 0

So I say: 1)0 is a lower bound of A, 2)$\forall x\in A \exists \epsilon>0 : x<0+\epsilon$

1/n is convergent and 1/n > 0

$x\in A$ so x is of the form $x=\frac{1}{n_x}, n_x \in \Bbb N$

Then $n_x>\frac{1}{\epslon}$

Can't use convergence, not yet taught,

But that last inequality doesn't hold for all n_x

What am I missing

@UserX You don't need a $\forall$, you need an $\exists$.

More precisely, you need $$\bigl(\forall \varepsilon > 0\bigr)\bigl(\exists x\in A\bigr)\bigl(x < \varepsilon\bigr).$$

Oh I got the forall and the exists backwards

So at the $n_x>\frac{1}{\epsilon}$ part I just choose a n_x?

@UserX Right. And you can do that because?

Because x is random?

My first guess would be n_x=frac(1/epsilon)

No, it has to do with some properties of $\mathbb{R}$.

I don't know why I can do that then... Why can I choose a n_x?

What properties of $\mathbb{R}$ do you know?

Completeness and density so far

Unless you include all the axioms

Completeness in which form?

If a subset of R is bounded then it must have a supremum

@UserX Good. so what about $\{ n \in \mathbb{N} : n \leqslant \frac{1}{\varepsilon}\}$?

That set has a supremum and an infimum.

The infimum is rather uninteresting. What about the supremum?

I think it's not bounded from above as epsilon can get really small thus n can be as large as we want it to be

@UserX $\varepsilon$ is a fixed positive number. It's arbitrary, but once you have chosen it, it's fixed.

Then 1/epsilon is an upper bound

@UserX Say $\varepsilon = \frac{2}{3}$. What is the supremum then?

Yea got that later

The sup has to be the largest n in that set

@DanielFischer sup of that would be 1

@UserX Right. Though we don't actually need that. What we need is that there is an $n_0$ in the set with $\frac{1}{\varepsilon} - \frac{1}{2} < n_0$.

(The $\frac{1}{2}$ is an arbitrary choice, anything larger than $0$ and smaller than $1$ would do.)

Then, what follows for $n_0 + 1$?

Its larger than 1/epsilon+1/2?

In particular, it's larger than $\frac{1}{\varepsilon}$.

I don't get what you're explaining to me right now

My problem or why I can choose a n_x

We need: $(\exists n_1 \in \mathbb{N})(n_1 > \frac{1}{\varepsilon})$. Because then $\frac{1}{n_1} < \varepsilon$, and hence $\varepsilon$ is not a lower bound.

@DanielFischer I still don't see a point...

@UserX You want to show $$0 = \inf \bigl\{ \tfrac{1}{n} : n \in \mathbb{N}\setminus \{0\}\bigr\}.$$ That $0$ is a lower bound is pretty clear. Now you need to show that it's the largest lower bound, or, that no $\varepsilon > 0$ is a lower bound. For that, you show that for every $\varepsilon > 0$ there is an $n_{\varepsilon}$ with $\frac{1}{n_{\varepsilon}} < \varepsilon$.

Hey

Ho

Hey

Yea, I got that far with a few(actually lot) more steps. What do I do now is where I got stuck in the first place.

Do I choose a $n_{\varepsilon}$?

@UserX Sort of. You show that, whatever $\varepsilon > 0$ is given, you can find such an $n_{\varepsilon}$.

Ok. So I choose a $n_{\varepsilon}=f(\varepsilon)$

I mean $n_{\varepsilon}$ has to have an $\varepsilon$ in it

I chose $n_{\varepsilon}=\frac{1}{[\varepsilon]}$. Is there a simpler one?

$[\varepsilon]$ is the fractional part of epsilon.

@UserX That's typically not an integer. $\bigl\lfloor \frac{1}{\varepsilon}\bigr\rfloor + 1$ would be a simple standard choice.

Damn I forgot I need it to be an integer

Hey @BalarkaSen I am gonna give a review for my topology class

I thought it would be a nice way to make sure I understand the material 100 %

Cool.

I got this homework question: "Service calls come to a maintenance center according to a Poisson process, and on average, 2.7 calls are received per minute. Find the probability that no more than 4 calls come in any minute." I know how to calculate Poisson probabilities. But since this is not specifying the number of minutes of the trial period would not the probability be 1 that 4 calls would come in a minute sometime?

For studying analysis of functions of several variables, which textbook will you recommend? I have heard some experienced learners and educators saying that the part of baby Rudin treating this topic (begin from chapter 9) is too abstract to know how to use the theorems...

@Tien-Cheng: That is not a particularly good part of Rudin. How advanced are you?

@TedShifrin I am a learner on undergrad level

But do you know all of Rudin's single-variable analysis, for example?

@TedShifrin I had studied Rudin's single-variable analysis part before joining 1-year compulsory military service in Taiwan. And after that I became somehow unfamiliar with the math I had learnt, so I am re-studying now.

I wrote a multivariable math book that has all the multivariable analysis in it, including differential forms and Stokes's Theorem. I also recommend C.H. Edwards' Advanced Calculus of Several Variables (published by Dover), and, if you're more sophisticated, Fleming's Functions of Several Variables (he includes Lebesgue integration).

@TedShifrin so it's recommended to complement the later part of baby Rudin with these books? thanks for your suggestion :)

You don't need all of the analysis in Rudin for Edwards, and you certainly don't for mine. For Fleming, probably most will be useful, especially for the integration theory.

I would not even read Rudin at all for the multivariable. And you don't need all the single-variable analysis to do multivariable. You need limits, continuity, open sets, compact sets, but not everything.

Answering decent questions gets no response; answering a fairly trivial question gets votes.

Off to the showers... BBL

Good hot afternoon in California @TedShifrin

hi @JulianRachman

Hello @BalarkaSen

how's things?

Great! You?

alright.

What you studying or working on now?

topology, calculus and algebra

mostly calculus

Multi or something else?

multivariable. don't know enough to learn forms.

Oh ok

What texts are you learning from?

Ted's book. "Multivariable Mathematics"

nice. And for Topology and Algebra?

Hatcher, Algebraic Topology and Atiyah-MacDonald + Reid + Eisenbud.

for commutative algebra.

nice.

I am currently studying category theory and starting Hatcher as well

meh. what's the point of learning category theory for the sake of it?

where are you in Hatcher?

For Aluffi's algebra

Not the best book on algebra, to be honest.

And as I said I am just starting Hatcher. So I am in technically the introduction

ah, I see. how much point-set have you learnt?

Then what do you recommend? Personally I do like Algebra 0 so far

I recommend Artin, as always.

Much more geometrically motivated.

ok

Aluffi talks about a bunch of cool-looking things but hasn't got enough hard exercises.

If you want good exercises, Dummit-Foote is nice. But don't read the theory from it.

And I have learned up to the requirement for point-set topology

How much? Do you know, say, the Tychonoff theorem?

i.e., quotient spaces, connectedness, etc.

no i do not know that theorem however I have heard of it

@JulianRachman uh-huh. where have you learnt these from?

Dugundji's text

ah, never read it.

I was recommended it by a professor at my local college the I personally read

@Julian if you want a gentler introduction to algebraic topology, look at Munkres part II.

Hatcher is generally considered a bit hard for beginners.

I started on Hatcher after Munkres, for one

Got the link?

Nope, hadn't had the time.

OK. Got it. I will try it out

gotcha

@JulianRachman what have you learnt in algebra?

Well I am still going through the category theory portion of the text

:(

however it starts with Groups right after

yes, I have seen it.

I am almost done with the category theory chapter. Then I will really be on my way

@Julian Here's an introductory problem in topology which will get you into fundamental groups and whatnot. Prove that $\Bbb R$ and $\Bbb R^2$ are not homeomorphic. Do you think you can generalize that to prove that $\Bbb R^2$ and $\Bbb R^3$ are not homoemorphic?

The first one is not hard. The second problem I don't expect you to solve it - maybe the best you can do (if you really can) is to provide a vague intuitive argument.

Worths a shot anyway.

OK, I am very sleepy right now and I need to get to bed. Catch you later.

Ok well I would say that my approach would be to prove this through finding that $\mathbb{R}$ and $\mathbb{R}^2$ are neither monomorphic or epimorphic

Alright. I will try to answer your question the later tonight. I will just tag you.