Many books, particularly in mathematics and related disciplines, contain sentences like "the proof is left as an exercise to the reader", which actually mean that the claim should be easy to prove for anyone reading until that point.  Can I write such a sentence in a paper submitted to a journal? Or will the reviewers consider it rude to omit a proof in such a way?
Possible arguments:  Pro   For brevity for trivial deductions   Contra   Looks like the writer could not be bothered to write an extensive explanation Definition of what is trivial to which reader and what not
Attending an academic conference is what type of travel? I am planning to travel to Portugal to attend an academic conference and in that regard needed a short-stay Schengen visa. The visa application has a field "Purpose of Travel" with the following options:   - Business - Sports - Cultural - Other - Study - Visiting family or friends - Medical reasons - Official visit - Transit - Airport transit - Tourism   I am attending the conference to present the research I am conducting as a part of my PhD. So "Study" is the closest in my opinion. But I don't want the Embassy to misconstrue that it is for studying at a university in Portugal. In that case, would "Business" be the right option to choose? Over time I realized a very annoying property of the Stack Overflow reputation system: Easy answers to popular question are rewarded with a lot more reputation points than actually great answers. In case anybody actually needs examples for this, here are two examples from :   gained me 420 rep, I invested 2 minutes writing it, and it only was a wild guess.   took me about an hour for the research and the math and gained me 40 rep.  Now I know that you are bound to get more rep for answers that are useful to more people, and I'd say that's fine. But the current situation is quite extreme: 30% of my reputation is from 5 of my 330 answers, and they are definitely far from being my best ones.  A final example that is not from my profile, but more extreme: Do you really think  is worth 40000 reputation?  My proposition to improve that situation would be to make the reputation gain from a single answer non-linear, maybe even have it capped at a certain point. I'm not sure on how that non-linear function should look exactly, and would leave good proposals for that to users with more experience than me. How to truncate a file in C? How to factor numbers that are the product of two primes A question about eigenvalues of $5\times5$ matrix $A\in M_5({R})$  and $A^2-4A-I=0$ If $a_1,a_2,a_3,a_4,a_5$ are eigenvalues of $A$ what is value of $$\left(a_1-\dfrac{1}{a_1}\right)+\left(a_2-\dfrac{1}{a_2}\right)+\cdots+\left(a_5-\dfrac{1}{a_5}\right)$$ I tried to work with $A^2-4A-I=0$ but get nothing because $A_{5\times5}$ characteristic polynomial is something like $A^5+k_1A^4+...$ Any hint will be appreciated . My computer name in System Preferences &gt; Sharing is set to &quot;archos&quot;, but is showing as &quot;iphone&quot; on Terminal. It just started doing this after I loaded Xcode for doing iPhone development: Last login: Mon Nov  7 14:46:55 on ttys001 iphone:~ travis$   Any ideas what could be causing this? Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$ There are lots (an infinitude) of smooth functions that coincide with $f(n)=n!$ on the integers. Is there a simple reason why Euler's Gamma function $\Gamma (z) = \int_0^\infty t^{z-1} e^{-t} dt$ is the "best"?  In particular, I'm looking for reasons that I can explain to first-year calculus students. Air friction at supersonic velocities How to keep processes running after ending ssh session? Let's say I launch a bunch of processes from a ssh session. Is it possible to terminate the ssh session while keeping those processes running on the remote machine? Question about the Riemann-Lebesgue Lemma proof Ok, so one of the formulations of the Riemann-Lebesgue Lemma says: $$ f\in L^1(\mathbb{R}) \implies \hat{f}(\omega)\to 0\;\mbox{ when } \;|\omega|\to\infty.$$  I get all the steps of the proof, except the one which says that if $f$ is an arbitrary integrable function, it may be approximated in the $L^1$ norm by a compactly supported smooth function $g\in L^1$. My question is: Why? How do you know that for all $\epsilon&gt;0$, and for all arbitrary function $f\in L^1$ exists a compactly supported smooth function $g$ so that $||f-g||_{L^1}&lt;\epsilon$? The "proof" can be found in many places, but this step can be found in Wikipedia Can a word be contracted twice (e.g. "I'ven't")? I commonly use the word 'guys' to refer to a group of males colloquially. It's colloquial but not rude, off putting, condescending, patronizing (though I wouldn't use it with a group of men at a board meeting (hypothetically of course), unless I knew them). So, some that I would not consider as replacements would be    buddies: too old-fashioned dudes: too informal boys: too patronizing men, gentlemen: too formal or false respect   I realized that I had also been using it for any group of people, males and females, even just females. It worked for me and I didn't think of the gender implications, that women might not care for it. No one ever complained, directly or indirectly (rule of life: sometimes people don't complain about things they should).   But it occurred to me (maybe by reading something that sparked realization) that the intended hearers might not all care for it.  What might be a female gendered or non-gendered version of 'guys'?  Some that I've considered don't feel right about (though these may be reasonable answers) are:   dolls: too old-fashioned babes: too informal  ladies: too formal or I've heard from women, too creepy women: too factual girls: too patronizing (as much as 'boys') everyone, you all: too bland y'all: perfectly non-sexist but too regional (might work, but not everywhere)   Hopefully I haven't eliminated all the possibilities -- any suggestions? How do I determine if a number is prime?  I'm writing a program where a user inputs any integer and from that the program determines whether the number is prime, but how do I go about that? $G$ a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K = \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$ I am trying to prove the following statement:     Let $G$ be a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K =  \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$.   From this, we get that $HK \cong H \times K$. Naturally, it would be ideal if I could prove that $HK \cong G$. One issue that I am facing here is the meaning of $G = \langle H, K \rangle$. How is this defined (I mean, more explicitly)? Is my strategy correct or How to put a unique material on duplicated objects separately? I've a sphere and then duplicated it. In object tree they are displayed as three siblings. I selected on of them and created a green glass material through node editor however this material was assigned to all three spheres. I confirmed that my selection is only on one sphere. What am I missing? How do you interpret a significant but weak correlation? Let $S = \bigoplus_{n\ge 0} S_n$ be a graded commutative ring. Let $f$ be a homogeneous element of $S$ of degree $&gt; 0$. Let $S_{(f)}$ be the degree $0$ part of the graded ring $S_f$, where $S_f$ is the localization with respect to the multiplicative set $\{1, f, f^2,\dots\}$. Suppose $S$ is finitely generated algebra over $S_0$. Then $S_{(f)}$ is a finitely generated algebra over $S_0$. Is it because Rey just saved BB-8 from a net, and then the droid just decides to follow her about - or is it for some other reason?  Does BB-8 have any idea who Rey is prior to being rescued by her?  Just wondering as she literally tells the droid to go elsewhere. Can you run Android in a VM on PC? I came across a how-to guide for running Android 1.7 in a virtual machine (VirtualBox), but 1.7 is old. I haven't been able to find a Android 2.2 or 2.3 image anywhere, does anyone have any ideas on how to virtualize newer Android OS's? Preferably a free virtualization solution like VirtualBox.  Here is the link about virtualizing 1.7:    They send you to here to download Android disk images:    But I can't find anything newer than 1.7, anyone have any ideas?