`from ... import` vs `import .`
Use 'import module' or 'from module import'?
How does MySQL store data Maximal ideals of polynomial rings in infinitely many variables Let $k$ be an algebraically closed field. Nullstellensatz states that the maximal ideals of the polynomial ring $R=k[X_1,\dots,X_n]$ are precisely those of the form $\langle X_1-a_1,\dots,X_n-a_n\rangle$, with $(a_1,\dots,a_n)\in k^n$.     What if we are working with infinitely many variables, say $\{X_i\}_{i\in I}$, being $I$ an infinite set? Again, the ideals of the form $\bigl\langle\{X_i-a_i: i\in I\}\bigr\rangle$, with $(a_i)_{i\in I}\subseteq k$ are maximal (even if $k$ is not algebraically closed), but what about the converse? Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$ I want to compute $$\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}.$$  Is it OK how I want to do?    $$\sin{\sqrt{x+1}}-\sin{\sqrt{x}}=2\sin{\frac{\sqrt{x+1}-\sqrt{x}}{2}}\cos{\frac{\sqrt{x+1}+\sqrt{x}}{2}}=2\sin{\frac{1}{2(\sqrt{x+1}+\sqrt{x})}}\cos{\frac{\sqrt{x+1}+\sqrt{x}}{2}}$$  I'm not surem but I want to say that $$|\cos \frac{\sqrt{x+1}-\sqrt{x}}{2}| \leq 1$$ $$\sin{\frac{1}{2(\sqrt{x+1}+\sqrt{x})}} \to 0 \mbox{ when } x \to \infty$$ So the limit is $0$ ?  I thinks is not because  if I say that $ \displaystyle|\sin{\frac{1}{2(\sqrt{x+1}+\sqrt{x})}}| \leq 1$ I will obtain that another limit than $0$.   Thanks :) Getting the Volume of an Uneven Mesh Show $f$ is analytic if $f^8$ is analytic This is from Gamelin's book on Complex Analysis.  Problem: Show that if $f(z)$ is continuous on a domain $D$, and if $f(z)^8$ is analytic on $D$, then $f(z)$ is analytic on $D$. (I assume the intention is that $D$ is nice, i.e. open and connected)  I'm not exactly sure how to approach this. I'm guessing it has something to do with zeroes of $f$. For example, around non-zeroes, $f$ is analytic since $z^{1/8}$ is nonzero in a neighborhood. Or something along those lines. The details are eluding me.  Any help would be appreciated! What licence is subscriber content provided under 4.0, 3.0 or them all? In the footer it says:     site design / logo © 2018 Stack Exchange Inc; user contributions licensed under  with . rev 2018.8.7.31273   However, in the footer under Company > Legal > '6. Content Permissions, Restrictions, and Creative Commons Licensing' it instead doesn't specify which CC BY-SA licence we're releasing our content under. It also links to the CC BY-SA 4.0 license:     The CC-BY-SA Creative Commons license terms are explained in further detail by , but you should be aware that all Public Content you contribute is available for public copy and redistribution, and all such Public Content must have appropriate attribution.   Since  if subscriber content is only provided under 4.0, where the footer says 3.0 it can cause users to break the licences.  The footer under Area 51 also mentions that content is licensed under CC BY-SA 2.5.  Since it's not defined which version of the license the content is provided under, I also interpret it to potentially mean all the versions.    What license is subscriber content licensed under? Arithmetic progression topology "Mornings came and cast a blinding sunlight over everything, and he felt like nothing worthwhile could be accomplished."  For some reason, I feel like "a blinding light" is ok, but if its sunlight, then I should drop the "a" and write "cast blinding sunlight", but I'm not sure why I feel this way.   Can anyone offer some enlightenment?  edit - alternate phrasing, closer to being a literal translation: "Mornings came without warning, flooding the day with a strong sun, and he felt like nothing worthwhile could be accomplished."   I would still like an answer to the technical question of whether I should drop the "a", but would also appreciate knowing if anyone thinks option #2 is a better choice. What are the survival limitations of alcohol? This question was inspired by watching one of the Pirates of the Caribbean movies; particularly where Jack Sparrow allegedly survives on a desert island by finding an unlimited supply of rum. I've heard alcoholic drinks dehydrate you more than hydrate you, so this seems like an unsustainable strategy.  My question is threefold.    How long can a human survive by drinking hard liquor (40% alcohol by volume) for their sole water intake (ignoring food)? If it's unsustainable, what will finally take you down? If the hard-liquor approach isn't viable, what % alcohol can keep you hydrated (beer, wine, etc.)?   Related: 1.  2. How do I disable negative scaling? By default blender allows you to scale past 0 - how do I prevent this?  i.e. it's common in other 3D modelling software to resize a set of vertices against an axis to align them - however this isn't possible when negative scaling is enabled. How Do I improve the performance of my Drupal7 Site? For somebody who is new to Drupal,  I see that there are many resources available on Drupal Caching but I am not sure which of them to use. So I have these two wheels parented to the leg of a robot. I wanna make them spin a few times but they're spinning around the wrong axis. With other objects I could just press R, Y, Y to make them spin right when they're already at an angle, but for some reason it doesn't work with these. Would be amazing if someone helped me fixing this! How do I determine the size of an object in Python? I want to know how to get size of objects like a string, integer, etc. in Python.  Related question:   I am using an XML file which contains size fields that specify the size of value. I must parse this XML and do my coding. When I want to change the value of a particular field, I will check the size field of that value. Here I want to compare whether the new value that I'm gong to enter is of the same size as in XML. I need to check the size of new value. In case of a string I can say its the length. But in case of int, float, etc. I am confused. Add a section before \tableofcontents to content How do I generate a smooth random horizontal 2D tunnel? I'd like to create a smoother version of the navigable and quite natural-looking random tunnel found in .  It should ideally be...   infinite, so more can be generated as the player progresses; parametrised, allowing control of its thickness over time; made of smooth curves, not rectangles as in the above game; precomputable, as knowing its bounds in advance allows collision detection for e.g. positioning powerups inside the tunnel.   I'm looking for a generic method I could implement myself. Further parameters and optimizations are welcome.  Asking here was suggested . I think this fits in both places, as it's as much about the algorithm as about gamedev. What does the comma operator do? Create an encrypted ZIP file in Python Pipe to multiple files in the shell I have an application which will produce a large amount of data which I do not wish to store onto the disk. The application mostly outputs data which I do not wish to use, but a set of useful information that must be split into separate files. For example, given the following output:  JUNK JUNK JUNK JUNK A 1 JUNK B 5 C 1 JUNK   I could run the application three times like so:  ./app | grep A &gt; A.out ./app | grep B &gt; B.out ./app | grep C &gt; C.out   This would get me what I want, but it would take too long. I also don't want to dump all the outputs to a single file and parse through that.  Is there any way to combine the three operations shown above in such a way that I only need to run the application once and still get three separate output files? What exactly is TLP doing that default system config wouldn't? All the info about TLP on the surface looks more like advertisement and marketing to me, I can't see any detailed comparison to default configurations. What are the precise differences compared to default (K/L)Ubuntu installs under the hood, are they really effective?  Update: And if they really are, why aren't they a part of a default config? Show that $\{\cos\ n:n \in \mathbb{N}\}$ is dense in $[-1,1]$ by using the fact below:      Suppose $x$ is irrational. Then there exists $p_n,q_n \in \mathbb{Z}$   such that $\bigg|x -\frac{p_n}{q_n}\bigg| &lt; \frac{1}{q_n^2}$   I have no idea on how to apply the fact above to show the set is dense in $[-1,1]$. Can anyone help me?