I hope everyone's weekend is going well. I had a long day yesterday. I took care of a lot of yard work, my son flew in from Chicago for the summer, and we had dinner when we got back from the airport. I was working on a question that got solved in pretty much the same way I was looking at it, so I needed to solve it another way. I need to stop working on questions with long answers. They take too long and usually get few votes.
@J.M.: how are things on Mma? I should pop over and look at what sorts of questions are being posted.
@robjohn Pretty good, I think. The activity isn't as frenetic as on math.SE, so it's much easier for me to catch up on questions I missed when I was away...
@robjohn I guess it depends on the topic. For the really specialized topics, the effort for writing is often in inverse proportion to the number of votes it gets. I've accepted it now, but it took me a long time to do so.
(That's why I'm conscientious enough to vote questions/answers on specialized stuff that I understand. For instance, I don't think there is a special-functions question that I haven't voted on (not counting mine, of course).)
@robjohn "much more rewarding personally." - and that's why I'm picky with questions myself. :D
@BillDubuque Hi Bill. Last time you saved me when I thought that prop. 3.11 in Atiyah-MacDonald was boring. Now I'm reading the chapter about composition series of modules. Can you save me again? I am not enjoying this chapter at all.
Do you think this case warrants temporary deletion? I sure hope so, as the number of people who stumble across that page in the next 2 weeks and are entering the competition probably far outweigh those not entering...
@JasperLoy I wouldn't say that I have taken anyone's opportunity for rep. Yesterday I was contending with joriki for a question, but he has 59k, so I don't worry about him :-)
@JasperLoy You did not mean basketball/football or something like this. Am I right?
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@robjohn I see you are quite serious about earning rep here. It is indeed an exciting game!
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@FrankScience Well, the humour comes from the possible naughty interpretation and the inherent ambiguity. As always, what I say in this chat may be interpreted in over 9000 ways.
@JasperLoy If I were serious about it, I wouldn't be answering the questions I do. Once in a while I take a breather and answer some lhf for a while, but most of my answers get only a small number of votes.
@JasperLoy and that is why we call you BabeLoy :-)
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@robjohn Hmm, I think those that get the most votes are usually simple but not too simple questions.
Like I don't get why I get 45 for like arithmetic progressions
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What happens here is just common sense. Psychologists take simple phenomena, apply technical terms to them and make it sound as if they know a lot about the human mind.
@JasperLoy well, I wasn't sure how to go with it. I wanted it to sound like Babylon but "Baby" would overshadow any intended meaning, but the main idea was the Tower of Babel. I wasn't sure if the "Babe" would have the same problem that "Baby" would. So I vacillated.
As for meds: I guess it's ok to feed pills to rats and see if they die and then only test it on hoomins if they don't.
@J.M. Well. I think you understand what I was saying. One manufacturer (owns the brands Iams and Eukanuba, cat & dog food) is famous for animal testing. Seriously, what pet owner can buy food for which pets have been tortured?
@PeterTamaroff I was searching for a link to the post of Eric that someone mentioned got upvotes due to an image being added. Do you know it? Aargh this browser is fried, can't see what I'm doing. Hold on a sec. Ok, I'm back.
@PeterTamaroff I'm not sure. JM wrote above "I knew Eric's answer in that thread would become highly rated if he added that picture, but not that highly rated..."
Because subsequent answers to analogous questions often seem to miss the innate symmetry. But perhaps those answerers never saw that (or related) threads. It's important to teach students how to generalize basic problem solving methods, to realize that a "trick" may be the genesis of a beautiful theory. But, alas, the SE software encourages fast answers, to the detriment of teaching.
@J.M. Quick question: if you take a beta blocker, how many days will it have a negative effect on your memory? I guess I could google it but if you happen to know that's a much faster way of finding out. : )
@PeterTamaroff I've got to do something, I'll be back in 10 minutes. Perhaps Matt can help you if he wants before then, if not I'll help when I get back. See you all soon.
@MattN. Well, now that I think more carefully about it, it was next week or something that I changed the avatar! I hope so, too. Thank you for your attention!
"Let $N$ be a nbhd if $a\in X$. Then $O\subset N$, where $O$ is an open set and $a\in O$. Since $O$ is an open set of the topology given rise from a metric, it is the union of open balls. In particular $$O=B(a;\delta_a)\cup \left(\bigcup_{x\in O}B(x;\delta_x)\right)$$
Now choosing $\delta<\delta_a$ $B(a;\delta)\cup \partial B(a;\delta)$ is a closed nbhd of $a$.
If N is a nbhd of $a\in X$ then $O \subseteq N$ where $O$ is an open set containing $a.$ We can find an open ball around $a$ with a radius small enough so this open ball is a subset of $O.$
Set that radius as $r.$ Then an example of the desired closed set is the closure of the open ball with radius $r/2.$
I don't think the only way to show that this set is a suitable candidate to prove the theorem is to use boundaries (if that is the concept with the theory not at hand now?)
@Gigili No, I can't empathise with this idea. Besides, if you kill someone you'll end up in prison. So instead of improving your situation you only make it worse.
Choose $\delta<\delta_a$. Then $\overline B(a;\delta)$ is a closed neighborhood of $a$ for $B(a;\delta) \subset \overline B(a;\delta)$ and the closure of a set is closed.
@Gigili I don't understand you. You said you were a religious person. But afaik, religious books such as the bible or the koran explicitly say that killing is a sin. On top of that, aren't you supposed to have faith and trust in G*d to make things better for you?
I'm gonna use the following statement in a research paper and am just wondering if it sounds mathematically correct. "As $u \to \infty$, this chance monotonically increases while being upper-bounded by a horizontal asymptote."
@PeterTamaroff Indeed, for example you seem to use the idea that open sets are unions of open balls almost every time you can, I implore you to place that in the back of your mind, it is far less useful that it seems.
@PeterTamaroff No, he goes to Australian National University in Canberra, I go to the University of Sydney, so most of the year we are in different cities.
@PeterTamaroff So let us just see how simple this problem can be:
We want to show that inside every nbhd, there is a closed nbhd of a point $a\in X.$ We draw a picture. We know we can draw an open ball around $a$ and a good candidate to be a closed nbhd would be the closed ball with half the radius, but we need to show that is indeed a subset. So we need to show $d(a,x)> r/2$ is impossible for points in the closure of $B(a,r/2).$ *Back to this in a second. With that, $d(a,x) \leq r/2 < r$ so $x\in B(a,r)$ as required.
@PeterTamaroff Anyway, it's almost 7am here now, I want to get at least 3 hours sleep before I start my next day lol. Good luck with your studies and even more so, your countries game against the US. Gnite all.
@robjohn Hmm :-). What was your first motivation for studying this? It is not really very harmonic analysisy or perhaps I don't really know about all of it :-).
@JonasTeuwen I actually started studying them when I had a program to test out a random number generator that set a random pixel on the screen. I wanted to find out how long it should take to fill a screen of $n$ pixels, and I computed $n\sum\limits_{k=1}^n\frac1k$ iterations.
@robjohn I think it does not. You have a sequence $p_n$ say the "probabilists's Hermite polynomials" and then you can verify they satisfy that condition. What do I miss?
