How can I deduce the existence of $2^X$ from the powerset axiom
(exercise from Tao's analysis book) Proof of a lemma relating to power set of X
Often (via Google Now, or when searching for a solution to some problem), I'll open a question from a non-favourite site in the app. Sometimes, I'd like to see what else is going on in the site where the question was posted. Currently, I have one of two ways:   Via tag icon:   Click one of the tag icons beneath the title Delete the [tag] text (at which point, thankfully, the sorting changes to Active from Votes).  Via manually searching for the site, which is more cumbersome. I type in hard and Hardware Recommendations is the fourth entry (below Ask Different, Raspberry Pi and Arduino)! This more annoying for meta sites, where I have to pick Meta from the dropdown menu.   Can I pretty please have a way to head to the site directly from the question? Maybe:   the site name in the top bar could become clickable and lead to the site, or an option in the More menu?     This would be especially useful for Meta sites, where questions posted around the same time could be related. Interestingly enough, most questions that Google Now are for metas of sites I visit on occasion, but haven't pinned to the list. Here's a screen capture from a site where I can view /site-analytics:    The orange "all posts" curve should be strictly larger than the blue "questions" curve, but they are mistakenly displaying the same data. Prove that a limit doesn't exist In my assignment I have to prove that the following function doesn't have a limit:  $$f(x)=\frac{x}{x-\lfloor{\sin x}\rfloor}$$ when $${x \to 0}$$  In other words, I have to prove that for every $\delta$ such that $0&lt;|x-{x_0}|&lt;\delta,$ $|f(x)-L|&gt;\epsilon$.  In fact, I don't even know how to start. Do I choose my $\delta$? I know that the sin function has certain values that's supposed to help me. How do I use it?  I have to prove this by definition, so I can't use limit arithmetic for example  Thanks. I have a site that is in French and English. I am able to successfully setup so that users can switch back and forth between the two domains to view either language, however I cannot seem to keep users logged in. When they are logged into the english domain and then switch to the french domain they are required to login again. However if they switch back to the english domain they are still logged in.  As an example we'll use www.english-domain.com as the base (default) domain and www.french-domain.com as the secondary domain  In settings.php I have modified the following, however it doesn't seem to be keeping them logged in. Am I missing something?  /**  * Drupal automatically generates a unique session cookie name for each site  * based on its full domain name. If you have multiple domains pointing at the  * same Drupal site, you can either redirect them all to a single domain (see  * comment in .htaccess), or uncomment the line below and specify their shared  * base domain. Doing so assures that users remain logged in as they cross  * between your various domains.  */ $cookie_domain = 'english-domain.com';   Note: That I have also flushed both site and browser cache as well as deleted any cookies left on my machine.  Update:  Here are my language settings: Generating a unique machine id How to take the gradient of the quadratic form? Please tutor the usage of patchcmd and xpatch I understand that the  package provides a command \patchcommand that can be used to add material at the beginning and/or end of the replacement text of an existing macro. It works for macros with any number of normal arguments but has limitations for macros with optional arguments.   was introduced to take care of the above limitations as well as provide some additional functionality.   Now, when I try to comprehend the usage of the above packages by reading the user documentations (, ), I get the feeling that they move to implementation details a little too quickly compared to other package documentations. There are not enough explanations or examples.  I also tried to grasp the concepts by reading the  and more or less understood whatever is presented there. However, that is not enough.  So, do you think we can ask for a complete tutorial on the usage of patchcmd and xpatch? Explaining the usage of the relevant commands like \patchcmd, \pretocmd and \apptocmd as well as, \xpatchcmd, \xpretocmd and \xapptocmd with sufficient examples should suffice. What does "no long range" mean on the soulknife rogue subclass mean? Create bootable CD from ISO Comparing StringBuffer content with equals Changing content of footline in beamer I have installed QGIS3 from the AUR package, as well as all optional dependencies:   However, when launching, I receive the following error:  Couldn't load plugin 'processing'   ModuleNotFoundError: No module named 'osgeo'  Traceback (most recent call last):   File "/usr/share/qgis/python/qgis/utils.py", line 311, in loadPlugin     __import__(packageName)   File "/usr/share/qgis/python/qgis/utils.py", line 664, in _import     mod = _builtin_import(name, globals, locals, fromlist, level)   File "/usr/share/qgis/python/plugins/processing/__init__.py", line 28, in      from processing.tools.dataobjects import *          # NOQA   File "/usr/share/qgis/python/qgis/utils.py", line 664, in _import     mod = _builtin_import(name, globals, locals, fromlist, level)   File "/usr/share/qgis/python/plugins/processing/tools/dataobjects.py", line 51, in      from processing.algs.gdal.GdalUtils import GdalUtils   File "/usr/share/qgis/python/qgis/utils.py", line 664, in _import     mod = _builtin_import(name, globals, locals, fromlist, level)   File "/usr/share/qgis/python/plugins/processing/algs/gdal/GdalUtils.py", line 35, in      from osgeo import gdal   File "/usr/share/qgis/python/qgis/utils.py", line 664, in _import     mod = _builtin_import(name, globals, locals, fromlist, level) ModuleNotFoundError: No module named 'osgeo'   Python version: 3.6.4 (default, Jan  5 2018, 02:35:40) [GCC 7.2.1 20171224]  QGIS version: 3.0.0-Girona Girona, exported   Python Path: /usr/share/qgis/python /home/thiago/.local/share/QGIS/QGIS3/profiles/default/python /home/thiago/.local/share/QGIS/QGIS3/profiles/default/python/plugins /usr/share/qgis/python/plugins /usr/lib/python36.zip /usr/lib/python3.6 /usr/lib/python3.6/lib-dynload /usr/lib/python3.6/site-packages /home/thiago/.local/share/QGIS/QGIS3/profiles/default/python   It seems to be a path issue, but I am not sure how to solve it. Pacman shows gdal and python-gdal both as installed. I have just finished my undergraduate studies. During last two semesters I've taken two subjects dealing with manifolds:   Analysis on manifolds, containing: definition of manifold, tangent space (as derivations and classes of curves), vector fields, vector bundles, flows, Lie derivatives, integration on manifolds (Stokes theorem), forms, Hodge decomposition theorem Introduction to differential geometry (for me it should be called introduction to Riemannian manifolds) containing: tensor calculus introduction, Riemannian manifold definition, connections, curvatures, geodesic, normal coordinates, geodesic completness theorem, classification throught curvature, jacobi fields, harmonic maps.    Now, for me differential geometry was/is a theory about manifolds, so anything dealing with manifolds is branch of differential geometry. On the other hand I am preparing for taking part in local conference called: "algebraic and differential topology".  I have read: ,  ,  , yet I still don't really know if differential topology is subtheory of differential geometry or is it seperate theory and how is it located between differential geometry and algebraic topology. For example I expect that studies on Riemmanian manifolds are part of differential geometry but would problem of classification manifolds up to diffeomorphism be a part of differential topology or geometry ?  Request: I would be grateful for your characterisation of differential topology and differential geometry possibly with examples of problems, theorems present at them. Can't see a glass object through another glass object in Eevee I've read a lot of conflicting advice on whether it's advisable to store eggs in the refrigerator. The case against seems twofold: (1) that eggshells are porous, and eggs can take on unwelcome flavours, or even spoil faster in the fridge, and (2) that cooking with cold eggs can be problematic. But lots of people refrigerate eggs through perceived necessity.  Do eggs last longer in the fridge, and is the shelf life gain worth it? Or should I just stick them in the cupboard? Redirect a portion of a bash script to a file to capture set -x output Problem numbering environment Why every polynomial over the algebraic numbers $F$ splits over $F$? I read that if $F$ is the field of algebraic numbers over $\mathbb{Q}$, then every polynomial in $F[x]$ splits over $F$. That's awesome! Nevertheless, I don't fully understand why it is true. Can you throw some ideas about why this is true? Consider the Fibonacci numbers $F(0) = 0; F(1)=1; F(n) = F(n-1) + F(n-2)$.  Prove by induction that for all $n&gt;0$,  $$F(n-1)\cdot F(n+1)- F(n)^2 = (-1)^n$$  I assume $P(n)$ is true and try to show $P(n+1)$ is true, but I got stuck with the algebra. How do we reach $P(n+1)$ from $P(n)$? Also, strong induction may be used instead. Can I get a postdoc in China more than 3 years after having received my PhD?