$\Delta$-Complexes Are Hausdorff
Prove that a topological space equipped with a delta-complex structure is Hausdorff
Can $\pi$ or $e$ be a root of a polynomial with algebraic coefficients? Since $\pi$ and $e$ are transcendental, neither can be the root of a polynomial with rational coefficients. However, it is easy to construct a polynomial transcendental coefficients (with $\pi$ or $e$ as one of it's roots), namely $(x-\pi)$ and $(x-e)$. However, is it possible to construct a finite polynomial (one of whose roots is $\pi$ or $e$) with only algebraic coefficients? (i.e. something such as $y=x^5-(\sqrt 2 -1)x^2+x$ .) A polynomial with only radical coefficients would be the best.  P.S. The polynomial doesn't necessarily need to have BOTH $\pi$ and $e$ as it's roots, just one is interesting enough. What is the opposite of "parallel" in architecture? The two towers of the Verrazano Bridge are not parallel: they are slightly [???] to account for the curvature of the earth.    What is that word? Pass in an array of Deferreds to $.when() I've got a utility that outputs a list of files required by a game.  How can I run that utility within a C program and grab its output so I can act on it within the same program? UPDATE: Good call on the lack of information.  The utility spits out a series of strings, and this is supposed to be portable across Mac/Windows/Linux.  Please note, I'm looking for a programmatic way to execute the utility and retain its output (which goes to stdout). How do I calculate my skill modifier? I'm trying to fill out the skills section on my first character, but when I look at the character sheets in the Starter Set as examples of how to make a character, the skills that are circled have higher modifiers than their Dexterity or Strength or whatever should make them.  I've filled out all skills but those. What do I add to the ability modifier to get those numbers?   My abilities are Strength 13, Dexterity 14, Constitution 11, Intelligence 15, Wisdom 8, and Charisma 8. Proficiencies are Arcana, Athletics, History, Investigation and Stealth. My saving throws are Strength and Dexterity.   I just started D&amp;D and have the Player's Handbook, DM's Guide, Monster Manual, and the Starter Set. Why can rm remove read-only files? If I create a file and then change its permissions to 444 (read-only), how come rm can remove it?  If I do this:  echo test &gt; test.txt chmod 444 test.txt rm test.txt   ...rm will ask if I want to remove the write-protected file test.txt. I would have expected that rm can not remove such a file and that I would have to do a chmod +w test.txt first. If I do rm -f test.txt then rm will remove the file without even asking, even though it's read-only.   Can anyone clarify? I'm using Ubuntu 12.04/bash. Where can I find every gnome? I'm learning JavaScript and while browsing through the jQuery library I see : (colon) being used a lot. What is this used for in JavaScript?   // Return an array of filtered elements (r) // and the modified expression string (t)    return { r: r, t: t }; Can't modify list elements in a loop When to use \par and when \\, \newline, or blank lines How can I get bash to perform tab-completion for my aliases? I have a bunch of bash completion scripts set up (mostly using bash-it and some manually setup).    I also have a bunch of aliases setup for common tasks like gco for git checkout. Right now I can type git checkout dTab and develop is completed for me but when I type gco dTab it does not complete.    I'm assuming this is because the completion script is completing on git and it fails to see gco.    Is there a way to generically/programmatically get all of my completion scripts to work with my aliases?  Not being able to complete when using the alias kind of defeats the purpose of the alias. Let $f$ be a nonconstant element of ring $\mathbb Z[x]$. Prove that $\langle f \rangle$ is not maximal in $\mathbb Z[x]$.   Let us assume $\langle f \rangle$ is maximal. Then $\mathbb Z[x] / \langle f \rangle$ would be a field. Let $a \in \mathbb{Z}$. Then $a + \langle f \rangle$ is a nonzero element of this field, hence a unit. Let $g + \langle f \rangle$ be its inverse. Then $a g - 1 \in \langle f \rangle$, hence $ag(x)-1 = f(x)h(x)$ for some $h \in Z[x]$, hence $ag(0) + f(0)h(0) = 1$, thus $(a,f(0))=1$ for all $a \in \Bbb Z$, contradiction, hence the proof.  Is my argument correct? Is there any other method? Why should the Standard Model be renormalizable? Effective theories like Little Higgs models or Nambu-Jona-Lasinio model are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These theories are valid until a scale $\Lambda$ (ultraviolet cutoff), after this scale an effective theory need a UV completion, a more "general" theory.  The Standard Model, as an effective theory of particle physics, needs a more general theory that addresses the phenomena beyond the Standard Model (an UV completion?). So, why should the Standard Model be renormalizable? If I'm on a page that has web notifications (like Slack or others), Firefox asks me if I want to enable them. However, my choices are "Yes" or "Ignore for now". The problem is, if I select "Ignore", every time there is a notification it asks me again. This is incredibly annoying.   How do I disable this completely? (I would accept disabling this feature entirely if that's easiest.) Exporting coordinates from LAS files to CSV? Is there any tool available for extracting the X, Y and Z coordinates from a .las file and exporting them to a .csv or similar file? Long rectangular quads? Or neat squarish quads with tris? For curved meshes I've often noticed that in my desperation to avoid tris, I tend to extrude the mesh in a way which creates these long rectangular quads:    In this case at least, the mesh is all quads, however the edge flow causes loopcutting to be awkward in some places:    I tried creating the same mesh with more even topology, however I found tris unavoidable. Maybe it was because I was starting with the long-quad mesh, but I also found myself using the knife tool for everything..    This makes loopcuts less necessary and easier to place in most cases, though the occasional tri does get in the way.  An annoying thing about the tris are the poles, though they aren't too noticeable in this particular case.    Both techniques seems to have their advantages and their disadvantages:    Which is considered "better", if any? Are there any better workflows for creating even topology with as few tris as possible? Or is there some trick I'm missing altogether? My understanding is that when using a Bayesian approach to estimate parameter values:   The posterior distribution is the combination of the prior distribution and the likelihood distribution. We simulate this by generating a sample from the posterior distribution (e.g., using a Metropolis-Hasting algorithm to generate values, and accept them if they are above a certain threshold of probability to belong to the posterior distribution). Once we have generated this sample, we use it to approximate the posterior distribution, and things like its mean.   But, I feel like I must be misunderstanding something. It sounds like we have a posterior distribution and then sample from it, and then use that sample as an approximation of the posterior distribution. But if we have the posterior distribution to begin with why do we need to sample from it to approximate it? Difference between $:=$ and $=$ I am sorry if this is quite elementary question. But I always think, that why we use $:=$ at some places, instead of $=$. Is there any fundamental difference between these two? Before reading Terry Tao's blog (4 months ago), I had never seen a symbol like this (:=). I accidentally killed the orphanage lady before I started the quest. She just pissed me off, sadly it will not acknowledge that I have finished the quest and I haven't been contacted. Is there another way to join the Dark Brotherhood? Welcome back message suggests to upvote questions and answers even when questions are locked I just opened a URL to a question on programmers.SE and got the message:     But the question was locked, so I couldn't do what it asked me to do.  I consider this to be a very minor edge case bug and it's likely not worth investing developer time into it. But since this  I guess it's worth reporting even if it's just for making you aware of it.