How do I holster weapons?
What is the proper way not to scare civilians?
How much will a poor first semester affect my grad school chances? When asking about , people sometimes refer to the strict aliasing rule. What are they talking about? Does Thanos's choice make any sense? So we know from Infinity War that Thanos was collecting all the Infinity Stones to basically solve the problems brought about by overpopulation on many planets.  But does it make any sense? He could've just easily increased the resources or changed the area or taken appropriate measure to handle that situation. As far as I know, collecting all the Infinity Stones gives the user limitless power and control over the universe in the MCU.  Is Thanos just a mass murderer or is there something I'm missing? Let $\{f_n\}$ be a sequence of analytic functions on a region $\Omega$ with $|f_n| ≤ 1$ on $\Omega$. Let K be compact and contained in $\Omega$. Suppose $\{f_n\}$ converges at infinitely many points in K. Then is it true or false that $\{f_n\}$ necessarily converges at every point of $\Omega$? How should a physics student study mathematics? Note: I will expand this question with more specific points when I have my own internet connection and more time (we're moving in, so I'm at a friend's house).  This question is broad, involved, and to some degree subjective.  (I started out as a physics-only student, but eventually decided to add a mathematics major. I am greatly interested in mathematics; the typical curriculum required for physics students is not deep or thorough enough; mathematics is more general (that means work!); and it only requires a few more classes. Naturally, I enjoy  immensely.)  This question asks mainly of undergraduate-level study, but feel free to discuss graduate-level study if you like.  Please do not rush your answer or try to be comprehensive. I realize the StackOverflow model rewards quick answers, but I would rather wait for a thoughtful, thorough (on a point) answer than get a fast, cluttered one. (As you probably know,  produces clear, useful writing; and a properly-done comprehensive answer would take more than a reasonable amount of time and effort.) If you think an overview is necessary, that is fine.  For a question this large, I think the best thing to do is focus on a specific area in each answer.    Update: To Sklivvz, Cedric, Noldorin and everyone else: I had to run off before I could finish, but I wanted to say I knew I would regret this; I was cranky and not thinking clearly, mainly from not eating enough during the day. I am sorry for my sharp responses and for not waiting for my reaction to pass. I apologize.  Re: Curricula:   Please note that I am not asking about choosing your own curriculum in college or university. I did not explicitly say that, but several people believed that was my meaning. I will ask more specific questions later, but the main idea is how a physics student should study mathematics (on his or her own, but also by choosing courses if available) to be a competent mathematician with a view to studying physics.  I merely mentioned adding a mathematics major to illustrate my conclusion that physics student need a deeper mathematical grounding than they typically receive.   And now I have to run off again. Do I need an ESTA if entering the US from Canada by train As a UK citizen, I will be flying to Vancouver (for which I will need an eTA) and then taking an AMTRAK train to Seattle. I will stay in Seattle for several days before returning to Vancouver and flying back to the UK. Do I need an ESTA for entering the US during this trip? Intuitive explanation for formula of maximum length of a pipe moving around a corner? Laptop w/o battery US bound flight? When working with radios, I've seen the term "dBm". What does this mean?  The  gives a table showing the equivalent power in Watts. Is the dBm output just the power level of a transmitter?  How does this differ from signal strength measured in dB? mod_rewrite to redirect URL with query string Are black hole regarded as baryonic matter in cosmology? Black holes do not have any property as baryonic or non-baryonic matter, as is stated by the no-hair theorem. Regarding conventional theories, in different models of cosmology, like Lambda-CDM, are black holes regarded as baryonic matter, and does the black hole matter significantly affect the baryonic density? Use of inequality $1 - \cos (x) \leq x^2 /2$ In  answer the value of $1 - \cos(x)$ has to be evaluated in order to find its upper limit, if it exists.  In particular, $x = 2 \pi / n$. The answer is related to the length of a side of a regular $n$-gon inscribed into a unit-radius circumference; because the perimeter of the $n$-gon is always less than $2 \pi$, the single side must always be less than $2 \pi / n$.  The inequality  $$1 - \cos (x) \leq \displaystyle \frac{x^2}{2}$$ (1)  is used and the proof is completed with   $$2(1 - \cos(x)) \leq (2 \pi / n)^2$$  $$\sqrt{2(1 - \cos(x))} \leq 2 \pi / n$$  But it is well known that the cosine is a function $f(x) \in [-1;1]$, so $1 - \cos (x) \in [0,2]$. By using this information, we would obtain  $$1 - \cos (x) \leq 2$$ (2)  The proof would provide  $$2(1 - \cos(x)) \leq 4$$  $$\sqrt{2(1 - \cos(x))} \leq 2$$  which is a completely different result.   Why in that case it is preferable to use (1) instead of (2)? How to choose when it is convenient to use (1) and when to use (2) in a proof? If I have a dataset with a very rare positive class, and I down-sample the negative class, then perform a logistic regression, do I need to adjust the regression coefficients to reflect the fact that I changed the prevalence of the positive class?  For example, let's say I have a dataset with 4 variables: Y, A, B and C.  Y, A, and B are binary, C is continuous.  For 11,100 observations Y=0, and for 900 Y=1:  set.seed(42) n &lt;- 12000 r &lt;- 1/12 A &lt;- sample(0:1, n, replace=TRUE) B &lt;- sample(0:1, n, replace=TRUE) C &lt;- rnorm(n) Y &lt;- ifelse(10 * A + 0.5 * B + 5 * C + rnorm(n)/10 &gt; -5, 0, 1)   I fit a logistic regression to predict Y, given A, B and C.   dat1 &lt;- data.frame(Y, A, B, C) mod1 &lt;- glm(Y~., dat1, family=binomial)   However, to save time I could remove 10,200 non-Y observations, giving 900 Y=0, and 900 Y=1:  require('caret') dat2 &lt;- downSample(data.frame(A, B, C), factor(Y), list=FALSE) mod2 &lt;- glm(Class~., dat2, family=binomial)   The regression coefficients from the 2 models look very similar:  &gt; coef(summary(mod1))               Estimate Std. Error   z value     Pr(&gt;|z|) (Intercept) -127.67782  20.619858 -6.191983 5.941186e-10 A           -257.20668  41.650386 -6.175373 6.600728e-10 B            -13.20966   2.231606 -5.919353 3.232109e-09 C           -127.73597  20.630541 -6.191596 5.955818e-10 &gt; coef(summary(mod2))               Estimate  Std. Error     z value    Pr(&gt;|z|) (Intercept) -167.90178   59.126511 -2.83970391 0.004515542 A           -246.59975 4059.733845 -0.06074284 0.951564016 B            -16.93093    5.861286 -2.88860377 0.003869563 C           -170.18735   59.516021 -2.85952165 0.004242805   Which leads me to believe that the down-sampling did not affect the coefficients.  However, this is a single, contrived example, and I'd rather know for sure. Update to latest version of java after ppa is discontinued I have been trying to install the latest version of java-8. However, I found out that the  due to changes in the java licence.  How should I update my java to 8.0_201 or 8.0_211 now?  Thanks! How can I check the actual size used in an NTFS directory with many hardlinks? On a Win7 NTFS volume, I'm using cwrsync which supports --link-dest correctly to create "snapshot" type backups. So I have:  z:\backups\2010-11-28\cygdrive\c\Users\... z:\backups\2010-12-02\cygdrive\c\Users\...   The content of 2010-12-02 is mostly hardlinks back to files in the 2010-11-28 directory, but there are a few new or changed files only in 2010-12-02. On linux, the 'du' utility will tell me the actual size taken by each incremental snapshot. On Windows, explorer and du under cygwin are both fooled by hardlinks and shows 2010-12-02 taking up a little more space than 2010-11-28.   Is there a Windows utility that will show the correct space acutally used? Chain-calling parent initialisers in python Using one group separator for integer part and another for decimal part (siunitx) I thought I was able to do something like this before, but I can't find my solution.  I would like to format my large numbers as follows:   12,504.3124 2359 3   I know I can use siunitx to partially set this up, but I'm not getting the results I want:  \documentclass{article} \usepackage{siunitx}  \newcommand\aenumA[1][4]{%%   \num[group-separator={,},        group-digits=integer,        ]}  \newcommand\aenumB[1][4]{%%   \num[group-digits=decimal,        ]}  \pagestyle{empty} \begin{document}    \aenumA{12504.312423593}    \aenumB{12504.312423593}  \end{document}   I would like a hybrid solution (commas in the integer part and spaces in the decimal).  I would actually also like to be able to group differently between the two: every three digits in the integer part, every four digits in the decimal part.  Is there a straight-forward way to do this with siunitx?  Or, do I need to split the number at the decimal and treat the two parts separately and then glue them back together? The choice between the gerund and the infinitive in a certain construction I am pretty much sure that for native speakers the issue I am going to bring up might look as an uncalled question as they can easily figure out which form of a verbal part of speech should be used, be it a gerund, an infinitive, or a bare infinitive. However, it can be pretty much misleading for a foreigner because the same construction works differently with different words and I don’t see a logical explanation. For example:  The purpose of this article is to analyze the issue…  My hobby is reading. One may assume, and many foreigners really come to this conclusion, that it’s OK to switch the “gerund” and “infinitive” as the meaning will stay the same, that is:  The purpose of this article is analyzing the issue… (same as 1 above)  My hobby is to read. (same as 2 above)   However, as I was told, this assumption is erroneous. Another example: His task was watching after them. (not good) His task was to watch after them. Is there any principle which governs the choice of the right form in such cases? Flawed proof that all positive integers are equal Is it possible to do a SELECT statement with a predetermined order, ie. selecting IDs 7,2,5,9 and 8 and returning them in that order, based on nothing more than the ID field?  Both these statements return them in the same order:   SELECT id FROM table WHERE id in (7,2,5,9,8)    SELECT id FROM table WHERE id in (8,2,5,9,7)