Given an infinite poset, show that it contains either a infinite chain or an infinite totally unordered set.
Prove that for any infinite poset there is an infinite subset which is either linearly ordered or antichain.
I have been using the default Ubuntu 11.10 with Unity for some time now and decided to start customizing it.  I have already been able to make some changes with the gnome-tweak-tool. However, there are many themes that I get from gnome-look.org that don't appear in the gnome-tweak-tool even after putting them in the /usr/share/themes folder.  Any idea why this is happening? Thanks. Consequences of a master thesis with errors I finished my master thesis 6 years ago, since then I gained a lot of experience on my field and also in academia. I can say that in that time I was a "child" , very inexperienced. I think that also my advisor did not help a lot, and I tried to do  a lot of things by my own, without someone to really review my things. Despite that, I still received a good mention by the master committee on final results.   Some days ago, I just decided to read part of master thesis, and I just realized a big nightmare coming. I identified a lot of typos, some references errors, and some improvements that I should do, but I did not. The worst thing is that I wrote a paper to a conference with my master thesis results (and some errors are there). The conference is not a high impact conference, but still the paper has my name and is available for everyone...   As I am finishing my PhD studies for now, I am concerning a lot that situation. My dream and goal is to pursue a Professor career. So, my questions are: What are (or could be) the consequences of a master thesis and paper with errors (some minor and some major) in academia? Revoke degree after years by errors in master is possible ( I am concerning a lot this situation that I thought on it)? How can I minimize it (I thought that I can put a fixed version of my thesis and paper in the future, for instance on my personal website)? How those errors can impact me in a Professor recruitment process?  Sorry for the long text, I am blaming myself all the time, and really afraid about the possibilities since I know that Academia career is really competitive. Setting proxy for apt from terminal I have desktop edition of Ubuntu.  I like the Terminal so that that I prefer to shutdown my computer with the shutdown command.  However when I type shutdown now it prompts me to enter my password.Is there any way I can shutdown my computer using this command without entering my password? Removing las2dem streaks from raster DEM? I've created a series of DEM files using the  tool from LAStools; however since I don't have a licensed version they have black streaks running across them. Does anyone know a good method for removing these streaks? Recursive function, if and which statements I have 1:50 wound current transformer and I don't have the datasheet. Could anybody help me to calculate the burden resistor?    Maximum current to be measured: 2A  Max output voltage to ADC: 5V How can I execute command on startup (rc.local alternative) on Ubuntu 16.10 I am setting up quota on my Linode server running Ubuntu 16.10, and I get the following error      Cannot stat() mounted device /dev/root: No such file or directory   So to fix this, I reached  for the fix which is done by adding   ln -s /dev/xvda /dev/root /etc/init.d/quota restart   to the /etc/rc.local. But Ubuntu 16.10 doesn't uses rc.local anymore instead uses . What is the alternative for rc.local, How can I run the above commands on startup?  Also I enabled the service using systemctl enable rc-local.service but it didn't work for me. Any lead would be appreciated. How to iterate over a comma separated list? How can I iterate, loop, process, or otherwise do something, with each element from a comma separated list of things?  This question       , and the are already lots of very good answers everywhere. However I think it would also be valuable to have a single reference point where all such alternative techniques are explained in detail, with their advantages and disadvantages discussed.  All of plain-TeX, LaTeX, LaTeX3, LuaTeX, Context, etoolbox, pgffor, etc. answers are invited. Please consider explaining, for example:   How does the command/method deal with whitespace around items? How does the command/method deal with empty/missing items? (e.g. a,b,,c) How does the command/method deal with a trailing comma? Can the command/method work of a list stored on a macro? Is each iteration evaluated globally or on a local group? (i.e., if a command is defined during an iteration, does the command survive the loop?) Do items get expanded or somehow mangled before being processed? What about lists where items are key=value or some other kind of pairs? Does the method work for lists separated with something other than a comma? Any other thing I should know before deciding to use this method? Using echo "20+5" literally produces the text "20+5".  What command can I use to get the numeric sum, 25 in this case?  Also, what's the easiest way to do it just using bash for floating point? For example, echo $((3224/3807.0)) prints 0 :(.  I am looking for answers using either the basic command shell ('command line') itself or through using languages that are available from the command line. Evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle I need to evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle.    Attempt: Let $\gamma(t) = e^{it} $ where $t \in [0,2 \pi]$. How can I get rid of the absolute values in the differential? Changing the keyboard layout turns off the numlock Not to Mention ≈ [Let Alone ≈ Much Less ≈ Still Less] For brevity, I symbolise synonymity with ≈.  So  X ≈ Y  means  X and Y are synonyms.  From : let alone ≈ not to mention  From :  let alone ≈ much less ≈ still less.  Are these all synonyms? What are the similarities and differences between each? Extracting tree crown areas from remote sensing data (visual images and LiDAR) Strange result when removing item from a list while iterating over it Strange bar plot alignment in Pandas Earning a PhD help you learn tools and techniques in your field, and lets you become an expert in a very specific field of science. However, once you get your degree and try to enter the labor market, you're competing against people who are younger than you (i.e. recently graduated non-phd engineers) and may have actual work experience (i.e. non-phd engineers with a few years in the market).  There are, of course, some positions in which they cannot compete, including research and teaching position. Those are the minority, though... in most other fields it seems that holding a PhD is not as important as (for example) work experience.  So, I would like to know:   Is work experience more important than having a PhD in the many work environments? What skills can I acquire/demonstrate during my PhD to become more "valuable" than a non-PhD candidate for the same job? Set of limit points of a subset of a Hausdorff space is closed. Let $X$ be a Hausdorff space and $A\subset X$.  Define $A'=\{x\in X\mid x\text{ is a limit point of }A\}$.  Prove that $A'$ is closed in $X$.  Relevant information:  (1.) Every neighborhood of a point $x\in A'$ contains a point $y\in A'$ distinct from $x$ (in fact, in a Hausdorff space, every neighborhood of $x$ contains $\infty$-many points of $A$ distinct from $x$)  (2.) In a Hausdorff space, every sequence has a unique limit.  On first glance, it should be an easy proof, but I've made little progress.  I was planning on showing $\overline{A'}=A'$.  Firstly, $A'\subset \overline{A'}$ trivially.  To show $\overline{A'}\subset A'$, proceed by contradiction.  Assume there exists $x\in\overline{A'}$ such that $x\not\in A'$.  This should yield an easy contradiction but I don't see it.  In particular, I'm unsure if the fact that $x\in\overline{A'}$ implies that there actually exists a sequence in $A'$ converging to $x$.  By (2) we know all sequences have unique limits, but do we know that elements in the closure are limits of sequences?  If this is true, it should yield an easy contradiction.  Any help? Why isn't .profile sourced when opening a terminal? Just installed Ubuntu 14.04.1 LTS.  According to .profile,  # ~/.profile: executed by the command interpreter for login shells.  # This file is not read by bash, if ~/.bash_profile or ~/.bash_login exists.   There is no ~/.bash_profile or ~/.bash_login.  It does not seem to source .profile when opening a terminal.   Why doesn't it source .profile when opening a terminal? Why is .profile there if it is not sourced? How do I know/control what is sourced when a new terminal is opened? When a new terminal is opened, does it do a "login"? Where is a good place to add $HOME/bin to my path? .bashrc? Will that cause a problem because .profile has the same code? Is there anything in the physics that enforces the wave function to be $C^2$? Are weak solutions to the Schroedinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't mention anything.