@AlessandroCodenotti Yes, I can. Consider $\{\frac{1}{n} ~|~ n \in \mathbb{N}\}$. I thought of this not too long after I left the chatroom. Taking walks have remarkable impact on mathematical progress. The example I gave generalizes in an obvious to the plane: $\{\frac{1}{n} ~|~ n \in \mathbb{N}\} \times \{0\}$
To stevedorenaut a boat by 4 canes 6,5 hours are needed. After 2,5 hours we can use one additional crane. How much time do we gain at the stevedorenaut?
Maybe they forgot to say it's $1$ for $\alpha = \beta$, in which case it's just saying isometries are local diffeomorphisms, which are by definition true.
Embarrassing because he is asking a question without giving enough information for us to understand what he means (or at least we have to deduce it). I tend to ignore such questions : if you're going to ask something, ask it well.
Ah ok. So, we know that the 4 cranes make 4/6.5 of the work in one hour. The first 2,5 hours we have 4 cranes so they have done 4/6.5*2,5 of the work. Then we can have 5 cranes. They make 5/6,5 of work per hour? @Astyx
I guess the next step is looking at the derivatives of $x(x(xx))$, $x((xx)x)$, $(x(xx))x$, $((xx)x)$, and $((xx)(xx))$. Which is too many for me. @Secret
Actually, although I don't believe in exercises, I believe in calculations. I think the first stage of math is where you do calculations, the second stage is where you do proofs, and the third is where you realise both calculations and proofs are important.
So, 4/6.5*2,5 of the work is already done. Let x be the hours that we have 5 cranes. Then the rest of the work is 5/6,5*x. When we add this (4/6.5*2,5+5/6,5*x) what does the result have to be? @Astyx
Demonark: Here's another terrible Jumble pun for you. "The flock of birds was sellings its roosts and hoped that other birds would ----" (7/4) HHMEESRPCET
They have to do what the 4 cranes make in 6,5 hours, so does this mean that $\frac{4}{6.5}\cdot 2.5+\frac{5}{6.5}\cdot x=\frac{4}{6.5}\cdot 6.5 \Rightarrow \frac{4}{6.5}\cdot 2.5+\frac{5}{6.5}\cdot x=4$ ? @Astyx
@Daminark I find that some exercises are just too specific and don't really show what is generally important. And the thing about important results being left to exercises, well, I think they should just be put in the main text instead. Maybe all the exercises I have been assigned to do weren't very good, which led me to have this viewpoint.
@Astyx Needless to say, as everyone in this chat knows, I am a fan of Lee and I like his three books on manifolds: Topological, smooth, and riemannian manifolds by John M Lee.
I would like to add that I use the PDFs for evaluation before deciding whether to buy a book, since I don't have access to a good library. But I think if one can afford one should buy the books to be fair to the authors and publishers, otherwise in future books will become extinct.
But yeah I rarely have one book I work out of fully, I just kinda bounce around and figure things out. That's a large part of why I prefer having some kind of class
I disapprove pedagogically of his making a big deal about real induction in the beginning Spivak course, DogAteMy, but he's stubborn. Nevertheless, it's interesting for more advanced students.
Or at least like, a reading group with other people where we're lecturing each other or something to that effect. I sorta need something more active, otherwise I'll lose focus quickly
Hello, I have this question let $(E,d)$ be a metric space and $\delta =\min(1,d)$ how to show that $(E,\delta)$ is bounded and what it's diameter ?please
@Balarka Lol, I am still not sure about whether I have some kind of ADHD or not. I know when I was younger my focus was capped at literally 3-5 seconds
@Jason I mean, so I don't know medicine and can't say whether ADHD is just, there's a spectrum and some people fall very low on it, or if there's a particular type of brain misfiring going on
Hello, I have this question let $(E,d)$ be a metric space and $\delta =\min(1,d)$ how to show that $(E,\delta)$ is bounded and what it's diameter ?please
@Daminark Hm, I don't have a clinically diagnosed problem, but I spend a day understanding very easy things. I just look at it, it looks hard at a glance, don't feel like understanding it, fiddle around, and come back to it and omg it's been 6hrs already!?!
@Daminark I am not a psychiatrist, but I have been mentally ill for many years and taken many meds. What I am saying is that some shrinks can help you, but most are quite stupid actually. The good ones know that they don't know much, the bad ones think they know everything.
@Daminark There are no biological or chemical tests in diagnosing most mental illnesses. They just give a label if your conditions make them tick a number of checkboxes.
I mean, for one, they studied the subject, at least more than I have, so I'm more or less categorically inclined to take the word of a psychiatrist over that of anyone else. And even the sophisticated ones, to my knowledge, acknowledge it
@Balarka So, I find that my issues tend to be of a similar sort. I tire quickly of technicalities/details, more than I ought, and until rather recently I was really bad at actually sticking to something for more than a bit, I'd just get frustrated and say "Well, next up!"
On some of the harder problems this quarter of analysis, I've actually stuck to things and come up with arguments I felt proud of, which only ever happened otherwise in graph theory/linear algebra with Laci (conclusion: I should move to Hungary)
@Daminark Yeah I suspect having concrete problem sets assigned to you helps, because you have that "goal" of finishing it than just doing random problems.
It helps for me, in any case!
That's why I have Ted and Mike to assign problems to me :P
@Astyx Well, the student version is 300 pages but it obviously contains much less material. It's A Student's Introduction to English Grammar. Both by Huddleston and Pullum.
@Jason That may be so, but it's mostly when I've done classes under Hungarian mathematicians that I've felt like I've actually done math. In the other quarters of analysis, and to some extent now in difftop, I've felt somewhat like the only arguments I've been able to generate were somewhat lame
@Daminark I somehow think that Germans are the best mathematicians. There are many good German math books, some translated into English already. I don't like the French and Russian ones so much. I hope that in my next life, I am born in Germany. It is my favourite country. =)
If you play scrabble, then you must have a big dictionary, like Chambers Dictionary or Collins English Dictionary. At least that's what they get in the UK.
@Astyx The Cambridge Grammar of the English Languages is really the holy grail of English grammar, there is no comparison to it. Don't confuse it with Cambridge Grammar of English, which is a totally different book.
@BalarkaSen Those goggles must let them see the solutions to the math exam.
Okay. I am asked to compute the 100th derivative of $p(x) = (x+x^5 + x^7)^{10}(1+x^2)^{11}(x^3 + x^5 + x^7)$. There has to be some clever way of doing this without expanding. I could use a hint, but only a hint please.
funny thing is that i disliked the movie after i watched it first time (didn't have taste for cult classics back then), but now i see how powerful a movie it really is
I am thinking of whether there is a good alternative to study axiomatic geometry. I know about Hilbert's book on the foundations of geometry but that book is ancient. Maybe I can just use Lee's book on that, but he doesn't do 3D.
@JasonBourne Haha...Well, the next problem is to compute the 99th derivative. So, either it is zero again, or the coefficient of the 99th term times $99!$ (I think), but I am not sure how to get that coefficient. I could use another hint.
@Ted so in geometry today neves gave a survey on all the big results of the type "curvature controlling topology" that he could think of. Seems kind of wild to me how many problems amount to not knowing whether or not a certain kind of metric exists on some space.
@user193319 Well, you just need to look at the coefficient of the highest term in the polynomial expansion and ignore the rest. That means the coefficient of x to the power of 99. What is that? That is, expand the polynomial first and then differentiate, not the other way round. But of course don't write down the entire expansion.
@Eric Will that be called something like comparison theorems in Riemannian geometry? I don't know.
