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12:00 AM
@hhh Yes.
 
hhh
Kindle Keyboard 3G
Source here, this one?
 
@hhh No no. Let me find it
@hhh This one
 
hhh
side-keys, for turning pages? They are missing in new kindles?
I cannot understand the 4G, it works country-independent?
No sim-card?
 
@hhh I think I can't really help you.
 
does anyone have a clue what this guy really wants?
 
hhh
12:16 AM
@JohnSenior I think one should explain him terms "translation" and "rotation"
and then proceed to simpler case where you modify things in the origin
then do necessary ajusting and then the backward operations
 
@hhh He talks about "linestring" and "polygonal buffer" ... does he really expect us to know what on earth he means? - and what does he mean by 0, 0, 10???
 
hhh
Point (0,0,10)?
 
@JohnSenior I smell a troll.
 
@PeterTamaroff Yes - or someone who has no clue about asking a question
@hhh and that relates to his diagram how exactly?
 
@AymanHourieh Are you there?
 
12:21 AM
@PeterTamaroff - Yes.
 
@AymanHourieh I answered your question.
 
@PeterTamaroff Wonderful! - does the OP have a hope of understanding the answer just postedf???
 
@AymanHourieh Let me sketch the proof for you.
Say $f$ is continuous at $[a,b]$-
Suppose, to argue reductio ad absurdum, that there is some $\epsilon_0$ such that there is no finite partition of $[a,b]$ where the oscillation on each subinterval is less than $\epsilon_0$
@AymanHourieh On a side note: finiteness of the partition has to do with "finite covers" and compactness, right?
 
@PeterTamaroff Yes, a finite partition corresponds to a finite cover.
 
Let $c$ be the midpoint of $[a,b]$. Then the theorem must fail either on $[a,c]$ or on $[c,b]$ or both. Let $[a_1,b_1]$ be the half where it fails. If it fails on both, let us agree to choose the left half.
Continue the process, letting $[a_{n+1},b_{n+1}]$ be the half of $[a_n,b_n]$ whee the theorem fails.
Note the oscillation on each $[a_n,b_n]$ is $\geq \epsilon_0$
 
12:27 AM
@PeterTamaroff This is the same idea used to prove that closed intervals are compact.
 
Let $A$ be the set consisting of $a,a_1,a_2,\cdots$
Let $\alpha = \sup A$.
Note $\alpha \in [a,b]$
THIS WAS THE PROBLEM: Since $f$ is continuous at $\alpha$, there is a $\delta$ such that in $(\alpha-\delta,\alpha+\delta)$ the oscillation of $f$ is less than $\epsilon$.
 
@PeterTamaroff Thanks for sharing. My first encounter with uniform continuity was through topology. It's interesting to see a similar but more elementary argument.
 
1:00 AM
where can i learn about lie groups and what are the prerequisites?
I just finished reading dummit and footes book
but there wasnt anything about lie groups on it?
where can i learn about them?
 
@MeAndMath Same thing I told ya last time. Why?
@Khromonkey I guess it's better to make a question for it.
 
@robjohn Oh, rob, thank goodness!
1
Q: Oscillation of a continuous $f$

Peter TamaroffThe original theorem is a as follows: THEOREM Let $f$ be continuous on $[a,b]$. Then for any $\epsilon>0$ there exists a finite partition of $[a,b]$ such that the oscillation of $f$ on each subinterval is smaller than $\epsilon$. The proof is as follows. PROOF We argue by contradicti...

 
Or search if some question already exists.
@PeterTamaroff Dude...
 
@GustavoBandeira Dawg?
 
I have an outspoken badge...
 
1:09 AM
@GustavoBandeira Can we be friends?
 
Yep. =D
 
@GustavoBandeira OMG OMG OMG OMG OMG
 
For serious - the word badge reminds me of Pokemón. It's the only thing I've seen the word badge. When I earn badges, I kinda feel this as a pokemon adventure. The moderators are the Gym Masters. Qiaochu is from elite four
 
@GustavoBandeira LAWL. I'm off to eat. If @robjohn drops by, make sure he sees my question!
 
@PeterTamaroff Your question about a pokemón battling?
 
hhh
1:19 AM
@PeterTamaroff I ordered "Kindle, 6" E Ink Display, Wi-Fi - for international shipment"Electronics; $89.00
 
are there good online books on differential geometry?
 
hhh
The cheapest and newest 12sept version, should be good enough even if it gets broken.
 
@PeterTamaroff My first AG question!
 
@hhh =)
@BenjaLim AG?
@BenjaLim I'm doing some calculus, but on disguise, I'm learning about compactness results =P
 
1:58 AM
@MarianoSuárez-Alvarez Estás? Justo llegue a la continuidad uniforme y la integrabilidad de functiones continuas!
Tengo un pequeño problema, igualmente.
 
2:10 AM
/me looks
 
@MarianoSuárez-Alvarez Estoy bastante seguro que estoy pasando por alto que $\alpha$ es el supremo.
 
since $f$ is continuous at $\alpha$
there exists a $\delta>0$ such that for all $y$ in $(\alpha-\delta, \alpha+\delta)$ we have $|f(\alpha)-f(y)|<\epsilon/2$
then when you pick two points $y$ and $z$ in that same interval, $|f(y)-f(z)|<\epsilon$
and therefore the oscillation of $f$ in that interval is at most $\epsilon$
 
@MarianoSuárez-Alvarez Just triangle inequality, right?
 
yes
(this has nothing to do with uniform continuity, btw!)
 
@MarianoSuárez-Alvarez And how does that statement differ from uniform continuity?
@MarianoSuárez-Alvarez Yes, I see =P
 
2:15 AM
it is completely different
notice that I used the continuity of f at exactly one point, $\alpha$
 
@MarianoSuárez-Alvarez Yes.
 
for all I care, in order to do this f could be discontinuous at all other points
 
@MarianoSuárez-Alvarez Uniform continuity says that for every $\epsilon$ there is a $\delta$ that works for every $x,y$ in a given interval, yes?
 
no
that is not what it says
 
2:18 AM
if you write that properly, it might be
:-)
but the statement you wrote is imprecise enough that it could be anything
 
If $f$ is uniformly continuous in $[a,b]$ then for every $\epsilon>0$ there exists some $\delta>0$ such that for any $x,y\in[a,b]$, $|x-y|<\delta$ implies $|f(x)-f(y)|<\epsilon$
 
OK.
@MarianoSuárez-Alvarez I was telling Jonas, the argument of bisection is amazingly useful.
Apostol used it 3 or 4 times already.
 
it surely is :-)
 
@MarianoSuárez-Alvarez here we need to chose $\delta=\min(\delta_1,\delta_2)$ where one delta is for $y$ and the other is for $z$, right?
 
2:27 AM
in the argument I wrote above?
 
@MarianoSuárez-Alvarez Yes.
 
then no
pick the delta as I said
it "works" for all points in the interval of width 2delta
now pick two points in that interval
&c
 
@MarianoSuárez-Alvarez is there anything special about the choice of $\alpha =\sup A$?
 
no
my argument depends simply on the fact that f is continuous at alpha
I proved that whenever a function f is continuous at a point a, for all epsilon there is a delta such that the oscillation of f in (a-delta,a+delta) is at most epsilon
 
@MarianoSuárez-Alvarez I mean in the proof of uniform cont. As far as I see, it assures $\alpha\in [a,b]$
 
2:33 AM
huh?
I don't know what you are talking about :)
the question you linked to has little to do with uniform continuity
 
@MarianoSuárez-Alvarez the one about the oscillation? Apostol calls it "teorema de continuidad uniforme" :confus:
 
well I did not say there is no relation
 
oh wait,no
 
but the question you linked to is independent of uniform contiuity
 
he says they are equivalent, sorry.
 
2:36 AM
the purpose of taking alpha in that way
is precisely so that he can reach the contradiction he reaches!
 
user19161
@PeterTamaroff As you may have already learnt from Mendelson et al, a continuous function on a compact metric space is also uniformly continuous, so that on the interval [a,b] continuity is equivalent to uniform continuity.
 
but that is a completely backwards way of explaining this, Will
 
user19161
@MarianoSuárez-Alvarez I was just throwing in a side remark for Pedro!
 
compactness and the theorem of uniform continuity on compact spaces is an elaboration
of this result
using it to explaining uniform continuity on intervals is pretty absurd :-0
 
@MarianoSuárez-Alvarez could you post that little $\epsilon /2$ proof as an answer so I accept and close??
 
2:41 AM
write it yourself! :-)
 
@MarianoSuárez-Alvarez =) OK! Could we arrange a meeting someday this week? Tomorrow maybe? Could it be?
 
this week I don't think so, because I have a guest from Brazil who takes aaaaalllllllll my time :-/
 
@MarianoSuárez-Alvarez Oh, OK.
 
user19161
@MarianoSuárez-Alvarez Must be a very important guest!
 
all guests are important :-)
 
2:44 AM
Can someone here help me understand this answer? Specifically the part in the spoiler.
 
urgh, I hate the spoiler thingie
 
@PeterTamaroff Argument of bisection? What does it mean? I think I know it, but not by name.
 
@JayeshBadwaik Step $1$: Get a big, sharp knife.
 
Becoming Dexter 101
 
@PeterTamaroff And then cut you with it if you don't give a good answer? I swear I will do that, if you mess with me right now.
:P
 
2:58 AM
@JayeshBadwaik JK. It is a tad long to explain and I'm busy, so you can prolly google it. It is past midnight here, and I have univ. tomorrow =/
 
user19161
@JayeshBadwaik It means that something must lie in one of two subintervals at least, and you keep cutting it up until you get a sequence of nested intervals.
 
@JayeshBadwaik Actually, if you want to prove theorem and someone claims it is false, use the knife repeatedly.
 
user19161
Showing that the intersection is nonempty then proves the existence of that something.
 
@MarianoSuárez-Alvarez New season comes out in a few weeks =D
 
@PeterTamaroff Okay. Just woke up hence a little cranky, no problem. Will see it.
:P
 
user19161
3:09 AM
@peter How do you find Apostol so far?
 
@WillHunting Superb.
Come at me bro.
 
user19161
@PeterTamaroff I think it is superb as well. Well done!
 
user19161
@PeterTamaroff Now that sounds gay! :)
 
@WillHunting Ugh! It is a challenge. Disgusting.
 
3:25 AM
it would probably be a good idea to cut down on the frequency of gay-themed jokes on this room...
 
@MarianoSuárez-Alvarez Yes, it turns out to get kinda offensive
 
user19161
@MarianoSuárez-Alvarez Yes, I agree.
 
@WillHunting For the record, I'm not encouraging this! :meanlook: @JonasTeuwen
 
user19161
@PeterTamaroff Oh yes, we three lefties are responsible for this, hehe.
 
I thought this guy was trolling
@WillHunting I disagree with that... I don't bring up the topic.
 
user19161
3:30 AM
@PeterTamaroff You do with the pics you posted. :-)
 
user19161
IIRC, there were two yesterday.
 
@WillHunting Hahaha, that one time, OK.
You got me.
@WillHunting But it was about Justin Bieber, not about people in the room.
 
user19161
@PeterTamaroff No, that was another occasion, and still the fact is, it falls into the same category. Anyway let's avoid this now.
 
user19161
@PeterTamaroff WTF is that?
 
3:39 AM
@PeterTamaroff Beautiful.
 
@WillHunting This room.
Bye byes.
@MarianoSuárez-Alvarez Thanks for the help. Hope we can meet soon.
 
user19161
@PeterTamaroff Good night! I will see you in your dreams.
 
@MarianoSuárez-Alvarez You and Pedro are at the same univ?
 
user19161
3:54 AM
@JayeshBadwaik Do your friends call you Jay?
 
@WillHunting Not generally, Jay is also an Indian name. But generally my mom and other close friends do.
Jay means victory. Jayesh means god of victory.
 
user19161
@JayeshBadwaik But how is it read? My or nay?
 
I call him Jay.
 
"Jai"
@WillHunting "Jai" if that makes it clearer to you.
 
user19161
@JayeshBadwaik So it rhymes with "my"?
 
4:00 AM
@JayeshBadwaik What's the meaning of Jayesh?
 
god of victory.
 
My name mean: The one who hold the stick
 
@WillHunting Not exactly. I will tell you the exact in a moment.
 
user19161
@JayeshBadwaik NVM.
 
@JayeshBadwaik How many vowels you have in your native languange?
 
4:01 AM
@GustavoBandeira Our structure is not of vowels and consonants.
 
Someone told me once that it has 7 vowels.
 
We have primary letters/sounds and then modifiers.
 
@JayeshBadwaik How's it?
 
Modifiers can be called as vowels though.
See, I will give you an example.
 
Endhiran!
=D
 
4:03 AM
"Endhiran"? Okay! It is actually a tamil word, but I can describe it I guess.
It is also pronounced as "Enthiran" which is more correct.
 
Gentleman, with you, Endhiran!
 
If that is a movie clip, then I have not seen that movie fully.
 
btw, are you still with dial up connection?
 
But it is surprising to know that you know about that film. Indian cinema seems popular.
Naah, :-)
 
user19161
I just lost 30 rep due to user removed...
 
4:07 AM
so it has the following structure "En + Dhi + Ra + N"
 
user19161
Who deleted his account?
 
user19161
@peter I thought you were sleeping!
 
Now, En is actually a modifier + a sound. It is "E + Na". The "E" is pronounced more in the manner of "A"
 
@WillHunting We can help you. Post a question, a silly one: "What's the name of my mother?", wait for two days, now @anon will place a bounty of 50 rep on your question. You answer it, you accept the question, problem solved. GG
 
what
 
4:09 AM
"I like math because it helps the development of my problem solving skill"
 
user19161
@GustavoBandeira That is SILLY.
 
also, user removed = -103 = 21 upvotes + 1 downvote. interesting...
 
user19161
@anon Ah, I must try to divine who it is!
 
btw, reading your explanation, Jay.
 
4:11 AM
@jay For the récord my name means rock or hard as Rock. Some also say it means rock as in "base" because of simón's role in the bible
 
@PeterTamaroff Hmm. Nice
 
@PeterTamaroff Youre not trying to extende the meaning of "hard as rock" to some personal properties, are you?
 
@GustavoBandeira No jokes on the topic please, we have had enough now.
And the pronunciation of "Na" is that of "Nu" in Numbers.
 
Andhiran?
 
Sorry I must have said "A" in the manner of "Ace"
 
4:15 AM
I've heard there are gazilions of religions in India, is it true?
Once I've also read something you said: In your country, every state speaks a different languange.
 
user19161
Hinduism is more like a collection of faiths and practices.
 
What's the reason of this lingustic displacement?
 
@GustavoBandeira The main factor is in India, people do not consider religions to be exclusive of each other, you can worship anyone you want anywhere as long as you do not hurt the community using it.
 
(I hope "displacement" is the right word)
 
user19161
@JayeshBadwaik I am a little confused by the names of all the gods by now.
 
4:17 AM
So you can worship Jesus, Allah and any Indian god at the same time, and no one will worry.
 
@JayeshBadwaik as if the religion were subjective?
 
@GustavoBandeira Exactly.
 
@JayeshBadwaik What would hurt the community?
 
@GustavoBandeira Using religion to start wars on other religions, restricting their freedom just because they are of other religions?
 
@JayeshBadwaik OMG!
THIS IS AMAZING!
 
4:19 AM
Modifying rules of state to specifically hurt one religion over another.
 
user19161
@GustavoBandeira I dunno what you mean, but all religions are not well-defined. They all have millions of interpretations.
 
I didn't think such kind of respect could exist in the world.
 
@GustavoBandeira We also have our fundamentalistic clashes ;-)
 
user19161
@JayeshBadwaik Well, there have been a number of religious fights there right?
 
And there has been a big caste system in India which has been as exclusive as religions in other places in the world.
 
4:20 AM
@WillHunting Yep, but at least in catholicism - as it's practiced in Brazil - there's a limited set to follow.
 
But all that happens is not mainstream, it is on the sides.
 
@JayeshBadwaik I want to ask you something, but I'm afraid of hurting you.
 
@GustavoBandeira Go ahead, I won't be hurt.
 
user19161
@GustavoBandeira What I mean is, any religious text can be interpreted in whatever way one chooses.
 
@JayeshBadwaik From what caste are you? I was afraid of hurting because I dunno how one feel with such question. If you don't want to answer, it's okay.
 
user19161
4:22 AM
Very often, people believe in whatever they wish to and then use "religion" to justify their beliefs and cause suffering to others.
 
@WillHunting While I was ~15 years old, I started to think about this: "If I'm born in Brazil, I have a big choice of being from n religion, If I was born in India, same thing" and this would extend from every place in the world. I imagined it as some kind of cultural legitimacy and started to ask myself: "Is there some kind of universal legitimacy?"
(I hope my words have some meaning)
 
user19161
@GustavoBandeira What man needs is to truly and deeply think about religion, but the world is too stupid and evil to do that.
 
What does cultural / universal legitimacy mean?
 
@GustavoBandeira I am not offended so do not worry. But it is not a polite question to ask in India, mainly because caste system has caused so many problems that it is thought to be the best to eradicate it, and hence any such methods to further strengthen it are not welcome.
As for my answer, Officially I am of a "Naavi" caste as such, which traditionally means barbers/surgeons since the two operations were related in past.
 
user19161
@JayeshBadwaik Interesting they are related. Cutting hair = cutting body?
 
4:27 AM
@WillHunting Even in europe they were related, for minor ailments, that is where the red/white sign over the barbers come from in Europe.
Red for blood, white for bandages.
The barber surgeon was one of the most common medical practitioners of medieval Europe - generally charged with looking after soldiers during or after a battle. In this era, surgery was not generally conducted by physicians, but by barbers. They often took up residence in castles where they also provided medical assistance to the rich and wealthy. In the British Isles in the Middle Ages Formal recognition of their skills (in England at least) goes back to 1540, when the Fellowship of Surgeons (who existed as a distinct profession, but still not "Doctors/Physicians" as they are thoug...
 
@anon I thought about cultural legitimacy as the set of things you believe because you were born in that place and absorbed that things as beliefs - you believe n because you've been taught so. The universal legitimacy would be something like "truth for all cultures".
At the present state, I extended some biological possibilities in my mind, and it's kinda messy up here.
Such kind of questioning is the main force behind my interest on logic, metaphysics and epistemology.
@JayeshBadwaik I'm happy this is being banned.
Some years ago our main public television channel (Globo) showed a novel in which one guy from a lower caste was in love with one girl from a higher caste.
@anon Do you have something to add/ask to my reasoning?
 
@GustavoBandeira It is not so simple! There is political mileage to be extracted from supporting certain communities :P :P It is going to be there for a while, after all it is/was a fact of the social structure in India. Nowadays almost no one cares about intercaste marriages, so differentiating people on basis of caste is going to be difficult in future anyway.
 
@GustavoBandeira Reasoning about what?
 
@anon Legitimacy.
 
But it will be slow death, I don't think it will happen in my lifetime., or may be it is.
 
user19161
4:31 AM
The idea of "respecting other beliefs" is silly on its own. Some beliefs are so evil and stupid to me that if I "respect" it, I would be evil and stupid myself.
 
@WillHunting Yep.
 
Clearly many attitudes and beliefs are present through superficial absorption rather than their reasonableness, whereas many sorts of attitudes and beliefs are relatively universal among cultures. Is that what you mean by your reasoning?
 
@WillHunting now about the gazllion gods, the concept is, that the universe is just a dream being dreamt by a formless entity called brahma. All the other entities come into existence by isolating some kind of aspect of brahma, kind of like the measurement of quantum system.
 
@WillHunting It's strange that such beliefs are usually locked on people - they believe their beliefs are true and there's no space for arguing/changing. This is one of my current fears, I could be doing the same.
 
So, there are three most powerful of them, brahma itself (which represents creation)
 
4:34 AM
@anon Yep. I want to build such a dicotomy, if it's possible.
 
Vishnu (which represents stability, static nature and preservation)
And Mahesh/Shiva (which represents the dynamic nature and destruction)
 
His name Brahma is weird for me (Here i'm using weird as a lack of better term touse.)
 
The concept of dynamics cannot be separated from destruction similarly the concept of preservation cannot be separated from stagnant/static. I intuitively understand it, I do not know how other people view it though.
 
user19161
The only "religious figure" I truly respect is Gautama Buddha.
 
@GustavoBandeira Which question are you talking about?
 
4:37 AM
@JayeshBadwaik We have a beer in Brazil that have his name.
 
@GustavoBandeira LOL
 
user19161
@GustavoBandeira Oh, I keep forgetting you are from Brazil.
 
So, these are the three basic aspects. Now after that, all the humans are some form of "instantitation" of brahma, where we come into being (Actually any object) by being essentially separated from the cosmic consciouness by isolating certain aspects of it.
Some of the humans have some extraordinary aspects which make them the superheros of their generations.
 
@anon nvm
 
4:39 AM
These people are then also worshiped as gods.
And hence, we have gazillion of gods.
 
user19161
@gustavo I hear the Brazilian women are very beautiful. Do you think so?
 
@WillHunting It's true for the rich ones.
 
user19161
@GustavoBandeira Well, rich people just spend more taking care of their looks.
 
Yep.
But it's kinda hard to tell. I still don't know what is a brazilian citizen. We're a colonized country, it means there's a lot of miscegenation.
 
user19161
Even race is more of a cultural concept than a biological one.
 
4:43 AM
Yep.
 
user19161
Ultimately, I just see everyone in the world as "humans".
 
They called "mexican" at league of legends.
 
Have any of you guys read "The Naked Ape" by Desmond Morris ?
 
Yes.
I've heard about it.
I bought it but still didn't read it.
Ah, hey.
Do you guys have tablets?
 
user19161
Only those which you swallow.
 
4:45 AM
Kinda puts in perspective all the issues surrounding our cultural ideas.
That and Carl Sagan's Dragons of Eden.
@GustavoBandeira No, I don't
 
@WillHunting I imagined me swallowing an Ipad. XD
 
The answer by both of them is almost invariably the same "evolution" :-)
 
@JayeshBadwaik I've had some talks with nearby people.
"Evolution" is a misunderstood concept.
 
user19161
@GustavoBandeira iPad
 
@GustavoBandeira ?
 
4:48 AM
It seems that evolution has more to do with "change" than "improvement"
@WillHunting I mistyped it to avoid copyright suits.
 
@GustavoBandeira Yes. That is correct.
 
Will, past participle of spread?
I guess "spreaded" does not exist.
 
user19161
@GustavoBandeira spread spread spread
 
user19161
come came come
 
user19161
You can also look up such things in dictionaries.
 
4:52 AM
@JayeshBadwaik Somehow, people think it has to do with improvement. I blame Pokemón for that, the cartoon spread the idea that the evolved creature had more power...
 
user19161
If anything, I find that over time, human stupidity has just changed in form and not quantity.
 
@GustavoBandeira Seriously! Hehe, pokemon cannot have that big effect. There were other factors I am sure, starting from Darwin's time.
@BenjaLim Hi.
 
user19161
@JayeshBadwaik ?
 
@WillHunting I know, but I'm on my notebook in my bed, in my mom's home. No mouse nor decent internet here. It's easier to ask to you since you're a walking grammar.
 
@anon Hey
@JayeshBadwaik
hey
@anon Do you know any good references on representations of maximal compact subgroups?
 
4:54 AM
I don't know anything good for specifically that.
 
user19161
@BenjaLim I thought you were the one studying Lie theory, not anon. :)
 
Out of curiosity, in what way does it matter if a subgroup is maximal, or a subgroup at all, in the context of studying a representation of it?
 
I really want to get pro at mathematics, so I can understand what you guys are talking about.
 
Well, I know what a representation is, what a maximal subgroup is, and what a compact subset of a topological space is, so in principle I know what I'm talking about... but only in principle :-)
 
user19161
@anon Maybe one has many representations of the big group and wants one such that it satisfies certain properties for the subgroup?
 
user19161
4:58 AM
I dunno, just a thought.
 
So, choosing a representation subject to a condition on a restricted rep. That's a possibility. You know much more mathematics than you let on, Mr. Hunting.
Just a general observation.
 
user19161
@GustavoBandeira I think you need to do basic stuff first and not worry too much about these things now.
 

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