I have two render camera objects in the scene, about to be three, I'd like to know how to switch between them as when I hit zero, it only enters the view of my frontal camera(the first one I placed.) is it possible to switch between them?
I have multiple cameras in a scene. What I want to do is to change which one is active. This way I can view the scene from different angles. How would I do this?
Equivalence of the definition of the Subbasis of a Topology I came to know about 2 definitions of a subbasis of a topology. 1. A collection of subsets of X viz. S is said to be a subbasis of a topology T on X if S covers X and the finite intersections of elements of the subbasis form the basis elements (H.L.Royden). 2. If we consider the all the topologies on X containing S, then their intersection is also a topology on X and it is the smallest topology containing S. Then S is said to be a subbasis of the smallest topology, and the topology is said to be generated by S.  Now I want to prove their equivalency, i.e. S is a subbasis of a topology T iff T is generated by S. I have tried in the way: First let T is generated by S. Then by 2nd definition T is a topology containing S. Let B be the set of all finite intersections of elements of S.Then S is a subset of B and B is a subset of T (as T is a topology). LET T1 be the collection of possible unions of elements of B, we will show that T = T1. After this I am not able to proceed. Also I am unable to sketch the converse part. If something is wrong, please let me know, and also I hope to get help. Thank You. I'm trying to update my system using apt-get, but it's giving me this error  Err http://bd.archive.ubuntu.com raring Release.gpg          Could not connect to bd.archive.ubuntu.com:80 (116.193.170.18), connection timed out Err http://bd.archive.ubuntu.com raring-updates Release.gpg   Unable to connect to bd.archive.ubuntu.com:http: Err http://bd.archive.ubuntu.com raring-backports Release.gpg   Unable to connect to bd.archive.ubuntu.com:http: Reading package lists... Done W: Failed to fetch http://bd.archive.ubuntu.com/ubuntu/dists/raring/Release.gpg  Could not connect to bd.archive.ubuntu.com:80 (116.193.170.18), connection timed out W: Failed to fetch http://bd.archive.ubuntu.com/ubuntu/dists/raring-updates/Release.gpg  Unable to connect to bd.archive.ubuntu.com:http: W: Failed to fetch http://bd.archive.ubuntu.com/ubuntu/dists/raring-backports/Release.gpg  Unable to connect to bd.archive.ubuntu.com:http: W: Some index files failed to download. They have been ignored, or old ones used instead.   I am not a Ubuntu master but I can understand this is not a computer error. Any clues on how to fix it? From my , I learned that all tag related info on profile will be updated daily at UTC 03:00.  However, something is wrong here. It's now UTC 05:00+, but my tag number, say 93 (c++) is not updated against yesterday. I am pretty sure about this and I did earn some more points throughout the day. Sorry for not be able to capture the screenshot yesterday, but I did check this number 10 hours ago (which belongs to yesterday, also 93).  Is there a bug happening here? Or updating time different?    UPDATE: As of 24 Jan, the tags are still not updated with the proper values.  UPDATE2: Fixed around 25 Jan, UTC 03:00, at least for me. So we learned telescoping series in class and I came across this question in my textbook and I tried to evaluate it, but I don't understand how to do it.   $$ \sum\limits_{k=1}^n\left(k \cdot k!\right) $$  According to the answers:  $$ \sum\limits_{k=1}^n\left(k \cdot k!\right) = (n+1)! - 1 $$  We learned how to simplify certain telescoping series using partial fractions but I don't have any idea on how to start this question. Derivation of a generalization of Mertens' Third Theorem. One of Mertens' Theorems states $$\prod_{p\le x}(1-\frac{1}{p})\sim \frac{e^{-\gamma}}{\ln(x)}.$$ I have seen a generalized version that states  $$\prod_{m&lt;p\le x}(1-\frac{m}{p})\sim \frac{c(m)}{(\ln(x))^m},$$ where $m$ is a positive integer and $c(m)$ is a real number that depends on $m$. How can I derive this result? Is there a way to find what the values of $c(m)$ are? Thank you very much. I've searched for multiple forums for this questions and have seen different answers but so far, nothing have worked yet even from the ones I've seen here.  I want to extract a single file from a tar to a different directory.  I've tried this:  tar xvf file.tar -C /home/dir/ filename   or this:  tar -x filename -f file.tar -C /home/dir   But got these errors respectively:  x filename, 14826 bytes, 29 media blocks. File -C not present in the archive. File /home/dir not present in the archive.   and:  tar: /dev/rmt0: A file or directory in the path name does not exist.   The first extracted the file but in the same directory, not to the folder I wanted. Proving Cauchy condensation test I have to prove the  by tomorrow and I am really unconfident about what I did:  $$\sum_{n=1}^\infty a_n\text{ converges } \iff \sum_{n=1}^\infty 2^n a_{2^n}\text{ converges}$$  I did the following:  Let $(b_n)$ be a sequence as follow: $b_{2^k+m}:=a_{2^k}$ with $k\in\mathbb N_0$ and $0\leq m&lt;2^k$.  It's $a_{n+1}\leq a_n$ and so $0\leq a_{n+p}\leq a_n$ for all $n,p\in\mathbb N$.  So $\sum\limits_{n=1}^\infty b_n$ converges by the majorizing series $\sum\limits_{n=1}^\infty a_n$. And it's $\sum\limits_{n=0}^\infty b_n=\sum\limits_{n=0}^\infty\sum\limits_{m=0}^{2^n-1}a_{2^{n+1}}=\sum\limits_{n=1}^\infty 2^{n-1}a_{2^n}$ so $\Rightarrow$ is done.  For $\Leftarrow$ consider $c_{2^k+m}:=a_{2^k}$ with $k\in\mathbb N_0$ and $0\leq m&lt;2^k$.  It's $|a_n|\leq c_n$ and $\sum\limits_{n=0}^\infty c_n=\sum\limits_{n=0}^\infty\sum\limits_{m=0}^{2^n-1}a_{2^{n}}=\sum\limits_{n=1}^\infty 2^{n}a_{2^n}$ and so $\sum\limits_{n=1}^\infty a_n$ converges by the majorizing series $\sum\limits_{n=0}^\infty c_n$.  Is this in form and content correct? Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$ Show that    $$1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$$   So, I use Fermat's little theorem, that is if $p$ does not divide $a$, then $a^{p-1}$ is congruent to $1$ (mod $p$). But I'm still confused. If $1^{p-1}$ is congruent to $1$ (mod $p$), $2^{p-1}$ is congruent to $1$ (mod $p$), and $p$ does not divide $p-1$, so $(p-1)^{p-1}$ is congruent to $1$ (mod $p$). How does that equal $-1$ (mod $p$)? ZFC + $\exists$ Standard model $\rightarrow$ Con(ZFC + $\exists \omega$-model) $ZFC + \exists V_\alpha$ model of $ZFC \vdash Con(ZFC + \exists$ transitive standard model of $ZFC)$  and then  $ZFC + \exists$ transitive standard model of $ZFC \vdash Con(ZFC + \exists \omega-model$ of $ZFC)$  For the first one :   We can always find a countable extentional $M \subset V_\alpha$ elementary equivalent to $V_\alpha$. Let $M&#39;$ be the mostowski collapse of $M$. $M&#39; \approx M$ so $M&#39;$ is model of ZFC. And because $M&#39;$ is countable and transitive then $M&#39; \in V_\alpha$ (since $H_{\omega_1} \subset V_{\omega_1}$ and $\alpha$ is surely far larger than $\omega_1$).   So $V_\alpha$ is the model of '$\exists$ a standard transitive model of ZFC'.  For the second one :   I don't really know how to do it... Does anyone have an idea ? Must I enter Europe with Schengen visa from the country where I applied? If I applied for a Schengen visa from "country A" and I got the visa but I had some commitments in "country B" and I have to finish it before going to Europe should I get back to "country A" to travel to Europe or can I use the visa from any where? Package natbib Error: Bibliography not compatible with author-year citations I have a basic tex file and a bibliography which is exported from Mendeley  However, when I want to cite in the author-year style, I get the error:   Package natbib Error: Bibliography not compatible with author-year citations. (natbib) Press &lt;return&gt; to continue in numerical citation style.  Any clue what's wrong?  Minimum working example:  \documentclass[letterpaper, 10pt]{article}  \usepackage[authoryear]{natbib} \usepackage{lipsum}  \begin{document}  \lipsum[1-4] \nocite{*}  \bibliographystyle{apalike} \bibliography{articles}  \end{document}    A snippet of my .bib library:  @article{shortcode, author = {Lastname, Firstname}, file = {:/path/to/file.pdf:pdf}, journal = {Journal name}, number = {xx}, pages = {x--xx}, title = {Title}, volume = {xx}, year = {xxxx}     } What does the explicit keyword mean? What does the explicit keyword mean in C++? Possible Duplicate:          I have tried using \text{\~{}} to draw a tilde in math mode. However, this only produces a superscript tilde.  I have looked around at many pages such as this one:   and surprisingly, I can't find where to draw a tilde in math mode (not under or above a character - just a single tilde character). If I just use ~, then nothing appears. What hardware does Ubuntu Touch support? Does anyone know the name of travel posters from the 1930s? I'm trying to include a file with a specific shape (cup) into another TikZ image, in order to use the cup as a "stamp" to draw more complex figure. The file is located in /usr/share/tikzit/shapes/cap.tikz  \documentclass{article} \usepackage[svgnames]{xcolor} \usepackage{tikz} \usetikzlibrary{decorations.markings} \usetikzlibrary{shapes.geometric} \pagestyle{empty}  \pgfdeclarelayer{edgelayer} \pgfdeclarelayer{nodelayer} \pgfsetlayers{edgelayer,nodelayer,main}  \tikzstyle{none}=[inner sep=0pt] \tikzstyle{node1}=[cap,fill=White,draw=Black]  \tikzstyle{simple}=[-,draw=Black,line width=2.000] \tikzstyle{arrow}=[-,draw=Black,postaction={decorate},decoration={markings,mark=at position .5 with {\arrow{&gt;}}},line width=2.000] \tikzstyle{tick}=[-,draw=Black,postaction={decorate},decoration={markings,mark=at position .5 with {\draw (0,-0.1) -- (0,0.1);}},line width=2.000]  \usepackage[graphics,tightpage,active]{preview} \PreviewEnvironment{tikzpicture} \newlength{\imagewidth} \newlength{\imagescale}  \begin{document} \begin{tikzpicture}     \begin{pgfonlayer}{nodelayer}         \node [style=node1] (0) at (-2.5, 1.5) {};     \end{pgfonlayer} \end{tikzpicture}  \end{document}   The code i want to include is the following:  \begin{tikzpicture}         \path [use as bounding box] (-2,-2) rectangle (2,2);         \begin{pgfonlayer}{nodelayer}                 \node [style=none] (0) at (0, 0.75) {};                 \node [style=none] (1) at (-0.5, 0) {};                 \node [style=none] (2) at (0.5, 0) {};         \end{pgfonlayer}         \begin{pgfonlayer}{edgelayer}                 \draw [in=0, out=90] (2.center) to (0.center);                 \draw [in=270, out=-90, looseness=0.75] (1.center) to (2.center);                 \draw [in=90, out=180] (0.center) to (1.center);         \end{pgfonlayer} \end{tikzpicture}   But it seems I miss how to specify the directory of cup. I get this error:     Package pgfkeys Error: The key '/tikz/cap' requires a value. I am   going to ignore this key.   It seems like I have to deal with tikzstyle or pgfkey, but I don't know how to specify an external file. What is the difference between a teaching assistant and an instructor? It seems to me that the terms "Teaching Assistant" and "Instructor" refer to a variety of positions. At some places, a teaching assistant is responsible for things like helping the actual lecturer by handing out papers, grading homework, etc., and instructors hold recitation sessions.  At other places, I saw the term "instructor" referring to the lecturer giving the course, while a teaching assistant is the person doing anything else (recitations, grading etc.).  Is there some widely accepted definition of the two positions?  For context: The question arose because I wasn't sure whether I'm using the correct terms in my CV -- I am a math graduate student, and I would like to make a distinction between jobs in which I only graded course assignments/final exams, and courses in which I held recitation classes* (and also participated in grading the final exams). Is it OK to use "Instructor" for the latter? What should the former be referred to as?  *In the course I'm currently teaching, the recitations are planned and written by the ones giving them (without the professors' supervision). Also, the people giving the recitations are not necessarily grad students (some already hold a PhD). I'm elaborating on that because from what I've seen, some of it could be relevant for the definition of the job. Email from IOS with attachments larger than 7.5Mb gets stuck in outbox and constantly tries to resend. Costs us hundreds in data fees What does the "static" modifier after "import" mean? What does this notification icon mean? Samsung s7