Every injection $f: A \to A$ for finite $A$ is surjective
Surjectivity implies injectivity and conversely
is there a way to get the option "Organize Desktop by Name" in Ubuntu 19.10 same as in 18.04? Is either "can" or "could" more polite? Spurious space above align environment at top of page/minipage It seems that the align environment adds additional vertical space if it starts at the top of a page or minipage.  Below are two pages, and two minipages (on Page 1), where the first page/minipage has text followed by an align* environment, and the second page/minipage starts with an align* environment, and note that the equations are still aligned.  Attempted Solution: The closest related question I found was:    I attempted to use the  at the above by adding \setlength\abovedisplayskip{0pt} (after the preamble as per ).  Although, this did move the equations up vertically, they were still vertically aligned:  And since the problem occurs at top of a page as well, I don't think this is related to  Question:  How can I adjust the align environment to automagically not have additional space at the top of a page or minipage? Is there a reason for this behavior, and perhaps should not be changed?  Code: \documentclass{article} \usepackage[showframe,paperwidth=3.5in,paperheight=2.2in,margin=0.5in]{geometry} \usepackage{amsmath}  \begin{document}%\setlength\abovedisplayskip{0pt} Top of Page 1 \begin{align*}% Text above at top of page  e &amp;= m c^2 \end{align*}  \hrule \begin{minipage}[t]{0.45\linewidth}     Top of minipage 1     \begin{align*}% Text above this minipage      e &amp;= m c^2     \end{align*} \end{minipage} \begin{minipage}[t]{0.45\linewidth}     \begin{align*}% No text above in this minipage      e &amp;= m c^2     \end{align*} \end{minipage}  \newpage \begin{align*}% No text above at top of page  e &amp;= m c^2 \end{align*} \end{document} No option to remove Bluetooth device in iOS Settings app? I would like to remove my Raspberry Pi from my iPhone 8 (running iOS 11.2.1) as a connected bluetooth device.  Normally, I would go into my Settings -> Bluetooth and select the Info button (a small blue circled "i") to show the "Disconnect" and "Forget Device" dialogs:    Unfortunately, iOS does not give me this option for my device. The bluetooth device list does not contain an "i" for the item, and there is seemingly no other way to disconnect.    How do I unpair this device if there is no button to trigger to the unpair prompt?  Due to work restrictions I cannot completely reset the device. Cauchy principle value of $\int_{-\infty}^{\infty}\sin(x)/(x-a)dx$ Hazard Function - Survival Analysis I just started taking survival analysis class and I'm stumped on this question.  Let $T_1,...,T_n$ random independent continuous variables, with hazard function of $h_1(t),...,h_n(t)$. $T=min(T_1,...,T_n)$. And we need to show that the hazard function of T is $\sum_j{h_j(t)} $  Any help or direction are welcome :) I have seen both usages.    Stay tuned on our Facebook page to know more  Stay tuned to our Facebook page to know more    But don’t know which one is more appropriate. Please help me figure it out. Thanks Best way to parse RSS/Atom feeds with PHP Complete local ring which is not complete valuation ring Complete valuation ring is obviously complete local, because valuation ring is always local ring. I would like to know the example of  Complete local ring which is not complete valuation ring  Any examples? I could find example of local ring which is not valuation ring, but the example ring is not complete. Thank you for your help. PHP - Get rid of notation I have a laptop that has Windows 8 which I use for playing Minecraft. However when using the inventory, I have to hold my mouse to drag and pick the items and I don't like that.   I have tried switching mouses but that didn't work, is this possible to fix? General formula for evaluating integrals of the form $\displaystyle\int_0^\infty x^ae^{-bx}dx$ We know that the needle that is used in a compass is a permanently magnetized ferromagnetic material and commonly steel is used.  If we used an unmagnetized iron needle instead, would it still align with Earth's magnetic field lines? If yes, how? How to match all occurrences of a regex Is there a quick way to find every match of a regular expression in Ruby? I've looked through the Regex object in the Ruby STL and searched on Google to no avail. This formula provides the $n$th term in the Fibonacci Sequence, and is defined using the recurrence formula: $u_n = u_{n − 1} + u_{n − 2}$, for $n &gt; 1$,  where $u_0 = 0$ and $u_1 = 1$.   Show that     $$u_n = \frac{(1 + \sqrt{5})^n - (1 - \sqrt{5})^n}{2^n \sqrt{5}}.$$    Please help me with its proof. Thank you. This lock notice about collaborative effort is partly misleading is locked  with the following notice:     This question and answer are a collaborative effort: if you see something that can be improved, edit it!    Except that while the answer can be edited because it's a Community Wiki question, the question itself  can't be, because it's locked. I don't know the reason why it was locked, but maybe the notice's text should be changed or omitted? (I have no opinion on whether the question should stay locked or not.) After some searching on stack / google I decided to ask this here, this is the second time I'm facing this issue this time with blender 2.8, previously with 2.7 and without a clue to how I got here.  Some of my objects appear hidden(10/12), and I can't seem to find a way to unhide them.  Solutions to the most common rookie mistakes seems to be   In local-view solved by pressing numpad / hidden by pressing H or Shift + H, unhiding with Alt + H   I'm not in local view, I can toggle visibility for 2/12 objects with Shift + H &amp; Alt + H, but the rest stays gray in the collection.  Last time I solved this by exporting the whole model as STL and importing it back again, I then had to re-group all the pieces but there must be a more simple solution.  Here's the .blend if someone wants to have a go at it: Which lenses should be included in a travel photography kit? On a crop sensor camera, e.g. Canon EOS 7D, what would be the best kit to travel with around Europe for a few weeks? My shooting style will focus on landscape, architecture, and general travel shots (of note would be my lack of interest for portraits).     Limit to around 1-3 lenses, and I prefer light ones.   Crop sensor camera chosen to save on weight over a full frame option. Question is open to all brands for general guidance, but I will be using a Canon body.   Cost is not a factor, I will rent the lenses I do not already own.   Quality is of paramount importance. I will not have a tripod.   I understand some may consider this subjective, but I do believe that for a crop sensor body, with weight as a consideration, and a limit to the amount of lenses, a true best kit can be determined. I have put a bounty on , however I don't see it appear in the  (also not when I'm not logged in).  Why is this. Aren't all bounty questions supposed to be visible there? Integrating $\int_0^1 \frac {\log(1-x)\log^2(1+x)}x \mathrm{d}x$ Question: Integrate$$\int\limits_0^1dx\,\frac {\log(1-x)\log^2(1+x)}x=-\frac {\pi^4}{240}$$   I'm curious as to if there is a way to integrate this. I've tried using integration by parts to get$$I=-\frac {\pi^2}6\log^22+2\int\limits_0^1dx\,\frac {\operatorname{Li}_2(x)\log(1+x)}{1+x}$$However, I'm not sure how to continue even further. The polylog in the second integrand seems a bit intimidating and I don't see how the first term even helps.