@QED I don't like him, but I don't find him bothersome too. I do like the fact that the mod team there is decisive enough to ban people, and then tell them to get the fsck out when the ban expires.
@QED I always find formal phrasing to be patronizing. It has the subtext of "I don't care enough about you to write in a friendly way, instead here is a predefined comment written in a cold and concise language."
There are some replies that are used quite often. For example, the first reply to many questions is a demand for a minimal example. These replies should typically include a link with additional information. So I thought that it might be useful to collect some standard replies for quick copy&p...
"We denote the finite field of order q as GF(q), although it is also denoted Fq by many." Damn you, Simeon Ball, why not just write Fq and spare me the aesthetic angst?!?
I'd like some feedback on this answer. Is it understandable?
I see. I'd just comment that the ramen-PBJ diet isn't exactly the healthiest, so mix your food up a bit... or get yourself some vitamin pills if you can't.
But those cost money, and I can get 5 packs of certain ramens for $1, and the PBJ is my neighbohr's food. :P But yeah, oranges and ham and canned foods I'm also getting. I'll figure things out eventually.
Hello folks, I saw that about 30% of users who had committed to the Mathematica proposal on Area 51 were active on Mathematics. Some of you might be using mathematica despite not having committed. In case people didn't know, the proposal was closed 2 days ago because it would drain users from Stack Overflow.
Some of us are trying to reason with Robert Cartaino and get him to reopen. If you feel that you might have use for such a site, please consider voicing your support
@yoda I was pretty shocked about the proposal suddenly going kaput myself. I don't buy the cannibalization argument... if anything, SO is way too big that it's likely there are Mathematica questions there that I can answer, but don't bother to look for.
@JM yeah... and as Verbeia pointed out in her answer, you can't claim that the site will drain users from SO and at the same time say that we're not big enough to sustain a site.
A dedicated site might be one way to get more users from MathGroup to participate
@ZhenLin ...and that site would be an avenue to learn. :) I picked up a lot of interesting math from math.SE over the past year I've been in it myself.
I would imagine a site would allow novices to pick up tips and tricks from slightly more experienced users.
@JM Well, it's a problem I've been struggling with ever since I took up Riemann surfaces: given a complex polynomial $f$ in two variables, how do I visualise the zero locus $f(x, y) = 0$?
@ZhenLin Ah, I didn't get that at once. Then yes, I think either of ContourPlot3D[] or RegionPlot3D[] should do the trick. I think there are a few visualizations of that sort at the Wolfram Functions site...
@tb Looks like it. :) Who wants to co-opt it as an FAQ?
@ZhenLin Here is one example. (Michael Trott is pretty creative with these.)
@robjohn In this question (link alert! :=)), I wasn't sure of how uniform convergence can be profitably used, so I made up an elementary answer.
I thought of Zarrax's method, but it feels like a bit of cheating. Having done all the work to establish uniform convergence, I feel I might as well go ahead and bound the integral directly. =)
Unless you made an explicit call to a function that depends on J/Link, it shouldn't have to...
Anyway, it seems Trott's "tetraview" plots would be right up your alley. Unfortunately, the code at the Wolfram Functions site is old and needs a bit of spit-polish.
@Dylan: We didn't have to prove Urysohn in our exam, but we were asked about whether the theorem could be extended to various situations... Question 22G here.
@robjohn Sorry about being sloppy, but for the purpose of the proof, I only want $e^{z - cz^2} \leqslant 1+ z$ for $|z| < \varepsilon$ for some definite constants $c$ and $\varepsilon$.
@Srivatsan you just write down the function. $$\varphi(x) = \frac{\operatorname{dist}{(x,A)}}{\operatorname{dist}{(x,A)} + \operatorname{dist}{(x,B)}}$$
@robjohn Well, thinking about it, it seems to me that you can do exactly the same trick: take a smooth $f \geq 0$ that vanishes exactly on $A$ and a smooth $g \geq 0$ that vanishes exactly on $B$ and put $\varphi = \dfrac{f}{f+g}$
@robjohn, I think this claim is correct: For $-\frac12 \leqslant z \leqslant 1$, we have $\exp(-z - 2z^2) \leqslant 1 - z \leqslant \exp(-z)$. I think the constant $2$ is unneeded though.
Well, if we wish to be pedantic, all of $\mathbb{N}^3, \mathbb{N} \times \mathbb{N}^2, \mathbb{N}^2 \times \mathbb{N}$ are distinct... but hey, they're all naturally isomorphic anyway. :p
I hate pictures, they are good for the first intuition but then I get completely confused by them. It is also a well known fact that a picture is not a proof outside of algebra.
@N3buchadnezzar: I presume you mean $\int_\mathbb{R}$. Yes, they are the same. Whether this is a triviality or a deep fact depends on what you really mean by these formulae...
Well, as a matter of convention, $\int_{-\infty}^{\infty} \cdots \, dx$ usually denotes a Riemann integral, while $\int_\mathbb{R} \cdots \, dx$ could be a few different things. It could be a Lebesgue integral, or it could be an integral of differential 1-forms.
@tb I think the point is what Asaf said. In the induction step OP knows that $N^k\times N$ is countable. He does not see the connection with $N^{k+1}$.
I've corrected a few homeworks and tests from elementary set theory. People claiming there (in disguise) that $(\forall x) Q(x)$ is the same thing as $(\exists x)Q(x)$. It is sometimes surprising, what students are able to miss....
@tb Well I tried my best to show why I don't consider them duplicate (which is basically the same reason in Asaf's comment), but it is ok to have different opinions.
Nevertheless, I have the feeling that some of the questions that were closed as duplicates were of the type: To me (or anyone experienced enough) it is obvious that answer to Question A follows easily from Question B. So I vote to close. But it is not always clear to everyone....
Hi @Srivatsan. From some recent edits I have the feeling that you and J.M. are on the crusade against displaystyle in titles...
@Srivatsan IIRC, when I read the question some time ago, my understanding was that it asks about correct amount of generality. Or when it is better to prove more general statements. But I would have to read the post once again.
But, well, I don't feel competent enough to judge usefulness of this question. Answering this question assumes that one is familiar with several areas of mathematics and is able to see relations between them and give a common generalization.
I think that there are more competent people (than me) it this forum, which should be able to answer it or at least to say, whether it can be answered in reasonable way.
@MartinSleziak Well, my impression was that many people read the post, found it interesting, but thought nothing useful could be said at this generality, and moved on. :) Hopefully I am proved wrong though.
@robjohn Yes, I was typing up a reply: @robjohn Thanks for confirming that. I have seen this exact statement -- with those constants -- being used (but they did not prove it). Good to k
@ZhenLin Yes. However, Riemann doesn't use ß in that publication at all (if I haven't missed anything). Gauss also used the double s in his publications. See e.g. here
@ZhenLin German orthography was only uniformized in the early 20th century by Duden (1901 and it became official in 1902). The ß was used earlier, of course, but completely interchangably with the double-s.
I found a blog post a while ago discussing the rules for ſ in the old typography of various European languages. It was incredibly subtle and complicated...
"The pre-1996 orthography encouraged the use of SZ in place of ß in words with all letters capitalized where a usual SS would produce an ambiguous result. One possible ambiguity was between IN MASZEN (in limited amounts; Maß, "measure") and IN MASSEN (in massive amounts; Masse, "mass"). Such cases were rare enough that this rule was officially abandoned; however, it is still simply unimaginable for a non-Swiss to enjoy alcohol "in Massen", probably leading to old use where necessary."
There are some replies that are used quite often. For example, the first reply to many questions is a demand for a minimal example. These replies should typically include a link with additional information. So I thought that it might be useful to collect some standard replies for quick copy&p...
The mathematica proposal at 89 commitments has disappeared without warning or trace.
Why has it disappeared? And why without prior warning?
