enumerate tag using the alphabet instead of numbers
How do I change the `enumerate` list format to use letters instead of the default Arabic numerals?
{5,15,25,35} is a group under multiplication mod 40 Show that the set $\{5,15,25,35\}$ is a group under multiplication modulo $40$. What is the identity element of this group. Can you see any relationship between this group and $\mathbb U(8)$?   I am very stuck on this question and I think my knowledge of abstract algebra is my liability at the moment. Right now I'm most confused by the fact that I learned: An element of a group of this nature must be relatively prime with the working mod.  Obviously here this is not the case, so I don't really know where to begin.  Do I need a Cayley Table?  Thanks. Create Case thread Id using Apex (SOQL limit-proof) There are many posts about creating Case threadIds with Apex, notably   As the posters have noted, the SFDC rules of the threadId are subject to change over time and the only reliable way that I've seen is to do   // To be replaced with a real case Id. Id caseId = '500c0000008kJL5';   List&lt;Messaging.RenderEmailTemplateBodyResult&gt; renderResults =   Messaging.renderEmailTemplate(null, caseId, new List&lt;String&gt;{'{!Case.Thread_Id}'});  System.debug('this is the Case Thread Id: ' + renderResults[0].getMergedBody());   HOWEVER ... The method call Messaging.renderEmailTemplate burns a SOQL ()  So you can't prepopulate your Cases in an afterInsert or beforeUpdate Trigger because a transaction can be up to 2,000 (Platform Events), up to 10,000 (direct Apex DML) or more, typically, 200 rows.  All of these are > 100 SOQL limit.     So, before I go to the trouble of doing this in a chained set of async   tasks; is there more recent thinking on this subject of creating ThreadIds? Expansion of $(1+\sqrt{2})^n$ I was asked to show that $\forall n\in \mathbb N$ there exist a $p\in \mathbb N^\ast$ such that $$(1+\sqrt{2})^n = \sqrt{p} + \sqrt{p-1}$$   I used induction but it wasn't fruitful, so I tried to use the binomial expansion of $(1+\sqrt{2})^n$ but it seems I lack some insight to go further.   Any hint is welcomed. Give us better search-by-score syntax tl;dr: Give the score search operator ability to change between greater than and less than.  I just noticed that searching for score:0 turns up only question with a score equal to 0. Searching for score:1 gives everything with a positive score. (&gt;=1) I can live with these. But here's the big one: score:-1. I would expect it to give all the negatively scored posts - there is a minus sign in there. But it doesn't. It gives all the posts &gt;=-1. Greater than? So, my  is that we get more granular search options for score. For example,  score:1 would show all posts with score == 1 score:1+ would show everything score &gt;= 1 score:0 would show all posts with score == 0 score:-1 would show everything score == -1 score:-1- would show al posts where score &lt;= -1  In short, the operator after the number would show which direction to go with the matching. A minus sign means less than, a plus sign means greater than. No sign means exact. When I upload an image to Stack Overflow, I cannot see my JPEG file in my post. It's all blank. I've tried it with different files, but gotten the same result. How do I redirect in a class sub-classing the EventSubscriber class? Task manager for Ubuntu If I have a sequence of .obj (or any other readable format) files created from my own simulation code (say cloth simulation), can I use the rendering capabilities of blender to generate a video?   Is there a way to set the material properties for frame 1 and use the same or rest of the frames while the corresponding meshes are imported afresh from that ones I provide? Prove the following equality using mathematical induction: Prove the following equality using mathematical induction: For any integer $n \ge 1$  $$\sum_{i=1}^{n} \frac{1}{i(i+1)} = \frac{n}{n+1}$$  I understand for the base base I need to have $n=1$. If I substituted $n$ for 1 and $i$ for 1 I would get   \begin{align} \sum_{i=1}^{1} \frac{1}{1(1+1)} &amp;= \frac{1}{1+1} \\ \sum_{i=1}^{1} \frac{1}{2} &amp;= \frac{1}{2} \end{align}  As for the inductive step, I inputted $n +1$ but it did not work for me because honestly I did not know what to do with the $i$ and what I should do next.  How would I go about doing the next step and an explanation for $i$ would be helpful. move file by list in file (with leading whitespace) How do you mass-delete emails in iOS Mail? I don't know if this is documented anywhere, but just to bring it to current attention… What should I do when the GETDEB repository is down? I'm trying to install programs/files from the getdeb repo but get a "check your internet connection" error.  Programs than I've tried include Qbittorrent and Mozilla-Plugin-VLC.    Through the terminal I get the following errors:  Err http://archive.getdeb.net/ubuntu/ natty-getdeb/apps qbittorrent amd64 2.8.2-1~getdeb2   Could not connect to archive.getdeb.net:80 (209.105.191.78). - connect (113: No route to host) E: Failed to fetch http://archive.getdeb.net/ubuntu/pool/apps/q/qbittorrent/qbittorrent_2.8.2-1~getdeb2_amd64.deb: Could not connect to archive.getdeb.net:80 (209.105.191.78). - connect (113: No route to host)   &amp;  Err http://archive.getdeb.net/ubuntu/ natty-getdeb/apps mozilla-plugin-vlc amd64 1.1.10-1~getdeb1   Could not connect to archive.getdeb.net:80 (209.105.191.78). - connect (113: No route to host) E: Failed to fetch http://archive.getdeb.net/ubuntu/pool/apps/v/vlc/mozilla-plugin-vlc_1.1.10-1~getdeb1_amd64.deb: Could not connect to archive.getdeb.net:80 (209.105.191.78). - connect (113: No route to host)   I'm not having any problems adding/removing other programs/files from my machine.  Is there a problem with GETDEB repo (and if so, is there any way to fix it on my end) or is there something wrong with my computer's configuration? In (non-relativistic) classical physics, if the temperature of an object is proportional to the average kinetic energy ${1 \over 2} m\overline {v^{2}}$of its particles (or molecules), then shouldn't that temperature depend on the frame of reference - since $\overline {v^{2}}$ will be different in different frames?  (I.e. In the lab frame  $K_l = {1 \over 2} m\overline {v^{2}} $, but in a frame moving with velocity $u$ relative to the lab frame, $K_u =  {1 \over 2} m \overline {(v+u)^{2}}$). Does Android hide some amount of RAM from the User? I bought a new tablet, but Android (2.3.1) shows that it has only 150MB free of 256MB, and it should have 512MB.  I checked the file /proc/meminfo, MemTotal information. It only shows 256MB. Is there a possibility that the Android "hid" 256MB of RAM from the user? For simple linear regression, the regression coefficient is calculable directly from the variance-covariance matrix $C$, by  $$ C_{d, e}\over C_{e,e} $$ where $d$ is the dependent variable's index, and $e$ is the explanatory variable's index.  If one only has the covariance matrix, is it possible to calculate the coefficients for a model with multiple explanatory variables?   ETA: For two explanatory variables, it appears that $$\beta_1 = \frac{Cov(y,x_1)var(x_2) - Cov(y,x_2)Cov(x_1,x_2)}{var(x_1)var(x_2) - Cov(x_1,x_2)^2} $$ and analogously for $\beta_2$. I'm not immediately seeing how to extend this to three or more variables. At some point in (I think) the 90s, I saw an episode of something like Outer Limits or Twilight Zone where nobody was allowed to have more than average intelligence. Smarter children had to wear headsets which inhibited them from being too intelligent, administering minor electric shocks if intellectual thought was detected.  I can remember a final (or near final) scene of somebody watching his suicide and being upset but not remembering why because of the headset.  Can anybody identify the show and episode? Related:   This is a subtly different question because I'm not asking whether there's a historical relationship between the two lineages.  I am asking this question because answers to these questions:      are making assumptions about the appearance of Padme while pregnant, the period of gestation, and appearance of newborn babies.  All of these presuppose that the "humans" of the Star Wars Galaxy are 100% biologically equivalent to us.   In fact, as far as I know, we don't actually know any of those facts from canon.   (Do we?)   All we know is that "human" children and adults look like us.  So, do we have any canon or out-of-universe commentary that tells us that Star Wars humans and Earth humans are biologically equivalent?  Another way to put this would be  If presented with a Star Wars human and a Milky Way human, would the best doctors or the best medical droids be able to distinguish them? Unable to correctly install pip3 using apt-get I am using Ubuntu 16.04, and was experiencing issues with my pip3. Specifically, when I attempted to uninstall a package via  sudo pip3 uninstall   I encountered   Traceback (most recent call last):   File "/usr/bin/pip3", line 9, in &lt;module&gt;     from pip import main ImportError: cannot import name 'main'   I attempted to resolve this issue by reinstalling pip3, specifically   sudo python3 -m pip uninstall pip &amp;&amp; sudo apt install python3-pip --reinstall   which succeeded. However, I no longer have a local version of pip3 at all  bash: /home/kurt/.local/bin/pip3: No such file or directory   Using which pip3 in a new terminal I find,  $ which pip3 /usr/bin/pip3   and attempting to use pip3 at all brings me  $ pip3 Traceback (most recent call last): File "/usr/lib/python3/dist-packages/pip/_vendor/__init__.py", line 33, in vendored     __import__(vendored_name, globals(), locals(), level=0) ImportError: No module named 'pip._vendor.pkg_resources'  During handling of the above exception, another exception occurred:  Traceback (most recent call last): File "/usr/bin/pip3", line 9, in &lt;module&gt;     from pip import main File "/usr/lib/python3/dist-packages/pip/__init__.py", line 13, in &lt;module&gt;     from pip.exceptions import InstallationError, CommandError, PipError File "/usr/lib/python3/dist-packages/pip/exceptions.py", line 6, in &lt;module&gt;     from pip._vendor.six import iteritems File "/usr/lib/python3/dist-packages/pip/_vendor/__init__.py", line 75, in &lt;module&gt;     vendored("pkg_resources") File "/usr/lib/python3/dist-packages/pip/_vendor/__init__.py", line 36, in vendored     __import__(modulename, globals(), locals(), level=0) File "&lt;frozen importlib._bootstrap&gt;", line 969, in _find_and_load File "&lt;frozen importlib._bootstrap&gt;", line 958, in _find_and_load_unlocked File "&lt;frozen importlib._bootstrap&gt;", line 664, in _load_unlocked File "&lt;frozen importlib._bootstrap&gt;", line 634, in _load_backward_compatible File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2927, in &lt;module&gt; File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2913, in _call_aside File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2952, in _initialize_master_working_set File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 956, in subscribe File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2952, in &lt;lambda&gt; File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2515, in activate File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2097, in declare_namespace File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2047, in _handle_ns File "/usr/share/python-wheels/pkg_resources-0.0.0-py2.py3-none-any.whl/pkg_resources/__init__.py", line 2066, in _rebuild_mod_path AttributeError: '_NamespacePath' object has no attribute 'sort'   However, I am able to execute without incident when typing sudo -H pip3 -v. Reinstalling pip3 from apt, e.g.  sudo apt-get install python3-pip --reinstall   has no effect. If anyone has any insight, or has encountered a similar problem, I would greatly appreciate any input on how to approach this problem. Success of Bernoulli trials with different probabilities How should I phrase an important question that I need to ask a professor? When needing to ask a professor about something important and potentially delicate, what is an appropriate way to phrase the question or write the email?  Examples include:   Requesting a recommendation letter Asking for exceptions to policy (e.g., ignoring a course prerequisite, rescheduling an exam) Asking if you can do research with them, join a group, get into a program Scheduling a meeting, exam, or defense Letting them know about a change of plans Letting them know about a life event affecting your work or studies (e.g., wedding, funeral, sickness, vacation)