There are infinitely many subsequences of a bounded sequence $(a_n)_{n \geq 1}$ which are convergent.
Help me understand the proof for Bolzano-Weierstrass Theorem!
Iridescence In Cycles? Is it possible to create an  shader in Cycles? Specifically for something like , , , etc.. Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction Building where clause based upon parameters Determine the Galois group of $\mathbb{Q}(\sqrt{a+b\sqrt{d}})$ Apex:OutputText to Currency Format from String Wrapper is there a way to pass a string to the &lt;apex:outputText&gt; so that it can be formatted as a currency or percent value?  Here's what I have inside a column of my visual force table:  &lt;apex:outputText value="{0, number, currecny}"&gt; &lt;apex:param value="{!row.values[1]}" /&gt; &lt;/apex:outputText   this gives me an error at runtime (when the visual force page loads), which I think may be some kind of type mismatch, where &lt;apex:outputText&gt; is expecting a Decimal or number but I am passing a string.  This is the error at runtime:     The value attribute on  is not in a valid format. It must be a positive number, and of type Number, Date, Time, or Choice.   Thanks Can I apply for a Schengen visa at a country where I'm not a citizen? If so, under what conditions? I'm a citizen of country A who would like to apply for a Schengen visa at a consulate in country B. When is this possible? I can't browse to any website using Safari; yet, Google Chrome and Firefox are working fine. The Mac App Store also reports that it cannot connect.  I am running OSX 10.7.2 on a 2011 MacBook Pro. Do subdomains help/hurt SEO? If I have example.com, and blog.example.com, do search engines see those as one site or two? Will using subdomains hurt SEO? I have some technical reasons why I can't use example.com/blog. Set a polygon's normal's orientation as the objects local rotation orientation (if every polygon is an object) The more I use Stack Exchange, the more it is getting a knowledge-base for me. All questions, that I need for later reference I mark as favorite. Now I need to store these pages locally on my laptop. It is really time-consuming:  I could use Ctrl+S on each favorite question page  on Linux: there could be a solution with wget -N -r -l 1 &quot;https://stackoverflow.com/users/1069083/rubo77?tab=favorites&quot;  this will download all favorite questions but it creates no correct index.html Another approach would be to use the  to automatically follow into all your Stack Exchange-accounts. But that would have to be somehow limited to only favorites links on your  in each stack. cross-platform: You would need a firefox-plugin that downloads links recursively but only within the favorite-area of the  in your stack  Additionally, I would like to  and Convert list of ints to one number? On , I have my favorite tags filter. I setup email notifications for it and now I'm thinking I overdid it on the frequency. Trying to change the settings, I clicked on the edit link in the email notifications box to the right, except nothing happens. There are no JavaScript errors and the HTML for the link is simply &lt;a class=&quot;edit&quot;&gt;edit&lt;/a&gt;. This seems like unfinished planned feature. Update: Using Chrome Version 29.0.1547.66 m Same on Firefox 23.0.1  Both edit links are not working. Further Update Events capture:  Update 2014-02-03: Here's what the subscription tab in the network profile looks like. I can't see my background image in the 3D view I try to set up an image as background for a basic blender tutorial, but it isn't visible.  This is the image I try to have as background: Cheat-proof online die roller? I am looking for an online die roller that works similarly to the following:   The GM provides a string identifier to the player. E.g., "gandalf attacks balrog #12"   The player enters the id on the roller site, which checks it for uniqueness vs the DB, then generates the results, lined to that id.   The GM can check the results by id.     An alternative implementation would be for the GM to request a range of pre-generated ids from the site and hand them out to the players for rolls. E.g., "please roll 5d8 with id #314159265"  Is there anything similar?  Notes and Clarifications:  As Thales Sarczuk inferred, this is indeed for "play by forum/email" games.  The idea is to have "verifiable" rolls, preventing "roll until you you get a good result" scenarios. However, it will be used on forums that are not gaming-specific so using plugins is not an option.  Thank you! Compute $\Gamma(2.7)$ All I know of the Gamma function is $$\Gamma(\alpha) = \int\limits_{0}^{\infty}x^{\alpha - 1}e^{-x}\text{ d}x$$ and the recursive formula $$\Gamma(\alpha) = (\alpha-1)\Gamma(\alpha - 1)\text{.}$$ A friend asked me to try to find $\Gamma(2.7)$. I assume this involves complex analysis, which I have absolutely no background on (except for the basic Euler formula). Using Wolfram, I found that  $$\Gamma(2.7) = e^{0.434821}$$ which suggests to me perhaps writing out $e^{-x}$ as a Taylor series: $$\Gamma(\alpha) = \int\limits_{0}^{\infty}x^{\alpha - 1}\sum\limits_{i=1}^{\infty}\dfrac{(-x)^{i}}{i!}\text{ d}x$$ but alas, this doesn't look helpful.  How does one derive that $\Gamma(2.7) = e^{0.434821}$? What does ;; do in sh? What is model identifiability? I know that with a model that is not identifiable the data can be said to be generated by multiple different assignments to the model parameters. I know that sometimes it's possible to constrain parameters so that all are identifiable, as in the example in Cassella &amp; Berger 2nd ed, section 11.2.  Given a particular model, how can I evaluate whether or not it's identifiable? What is the physical significance of the off-diagonal moment of inertia matrix elements? The tensor of moment of inertia contains six off-diagonal matrix elements, which vanish if we choose a reference frame aligned with the principal axes of the rotating rigid body; the angular momentum vector is then parallel to the angular velocity. But while considering the general case, what are the off-diagonal moment of inertia matrix elements? That is, do they have any physical significance as [say] the components of a vector? Or is it merely a mathematical construction with no definite physical meaning (which seems rather wrong to me)?  A similar thread exists  but they are more interested in the principal axes of the body. It also says:     The physical significance of the off-diagonal components is that   you're using a coordinate system not aligned with the principal   directions of the object. They tell us nothing interesting about the   object itself.   Is that all or is there more to it, perhaps related to properties of tensors in general? Is it possible to embed a pre-existing DLL into a compiled C# executable (so that you only have one file to distribute)? If it is possible, how would one go about doing it?  Normally, I'm cool with just leaving the DLLs outside and having the setup program handle everything, but there have been a couple of people at work who have asked me this and I honestly don't know. ASP.NET MVC controller actions that return JSON or partial html I am trying to create controller actions which will return either JSON or partial html depending upon a parameter. What is the best way to get the result returned to an MVC page asynchronously?