I'm still a student and something funny that I've seen is that many mathematicians evade the question, "What is mathematics?" And when they don't evade it, every person gives a different definition. So I was wondering, and I think this is the best place to ask: What is mathematics specifically?   I think it is a very curious question and I just want to see what you think.
we all study mathematics , and all of us learn mathematical methods to solve problems , we learn how to prove , how to think mathematically   but the question is, what is mathematics ? how can we define it as a branch of science ?
How do I add this extra partition to my installed Ubuntu system? I started installing Ubuntu by watching a video tutorial about doing a disk partition installation, for that, inside Windows' 7 own disk partitioning tool. After a defrag I cut 100GB that I pretended to use on my Ubuntu installation for a little try out, now, while installing, I never really chose where I wanted Ubuntu to be installed, so I guess it just made a partition by itself of the minimum that the installation tells you it needs.  How can I now give the other 92 GB I had left apart only for that task?  Here's what my partitions look like now.     Here's a df:    And here's the GParted tool un ubuntu: Visiting USA as a German with Iranian parents I need help with a specific command that I am using in a new game that I am creating inside of Minecraft. The command is:  /give @p sign 1 0 {BlockEntityTag:{Text1:"{"text":" [MF2]","color":"gold","clickEvent": {"action":"run_command","value":"tellraw @a [""{"text":"[MF2]  ","color":"gold"},{"selector":"@p","color":"dark_aqua"},{"text":" is now an admin of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join Admin","color":"dark_aqua","clickEvent": {"action":"run_command","value":"scoreboard teams join admin @p"}}"},display: {Name:"Custom Sign"}}   If I take out the /tellraw command then the command works fine, but I need the command in there to announce to the game that a new admin has joined.  With the tellraw command, the error message is the following:  Data tag parsing failed: Unexpected token 't' at: text":" [MF2]","color":"gold","clickEvent":{"action":"run_command","value":"tellraw @a [""{"text":"[MF2] ","color":"gold"}, {"selector":"@p","color":"dark_aqua"},{"text":" is now an admin  of the server!","color":"white"}]"}}",Text3:"{"text":"Click to join Admin","color":"dark_aqua","clickEvent": {"action":"run_command","value":"scoreboard teams join admin @p"}}"   If anyone knows how to fix this, please let me know. Simple enough question: What math should all game programmers have a firm grasp of in order to be successful?  I'm not specifically talking about rendering math or anything in the niche areas of game programming, more specifically just things that even game programmers should know about, and if they don't they'll probably find it useful.  Note: as there is no one correct answer, this question (and its answers) is a community wiki.  Also, if you would like fancy latex math equations, feel free to use . Can't boot into Ubuntu in Windows 10 / Ubuntu dual boot Windows 98 on a modern computer? Order of elements in $Z_n$ I have this question:     Let $x, n$ be integers with $n \geq 2$ and $n$ not dividing $x$.  Show that the order o($\bar{x}$) of $x \in Z_n$ is   $o(\bar{x})= \frac{n}{HCF(x, n)}$   I've been thinking about it for ages but I still don't get why. A hint would be appreciated. If $\sum a_n b_n <\infty$ for all $(b_n)\in \ell^2$ then $(a_n) \in \ell^2$ I'm trying to prove the following:     If $(a_n)$ is a sequence of positive numbers such that $\sum_{n=1}^\infty a_n b_n&lt;\infty$ for all sequences of positive numbers $(b_n)$ such that $\sum_{n=1}^\infty b_n^2&lt;\infty$, then $\sum_{n=1}^\infty a_n^2 &lt;\infty$.   The context here is functional analysis homework, in the subject of Hilbert spaces.  Here's what I've thought:  Let $f=(a_n)&gt;0$. Then the problem reads: if $\int f\overline{g}&lt;\infty$ for all $g&gt;0,g\in \ell^2$, then $f\in \ell^2$. This brings the problem into the realm of $\ell^p$ spaces.  I know the inner product is defined only in $\ell^2$, but it's sort of like saying: if $\langle f,g\rangle &lt;\infty$ for all $g&gt;0,g\in \ell^2$ then $f\in \ell^2$.  I read this as: "to check a positive sequence is in $\ell^2$, just check its inner product with any positive sequence in $\ell^2$ is finite, then you're done", which I find nice, but I can't prove it :P  From there, I don't know what else to do. I thought of Hölder's inequality which in this context states: $$\sum_{n=1}^\infty a_nb_n \leq \left( \sum_{n=1}^\infty a_n^2 \right)^{1/2} \left( \sum_{n=1}^\infty b_n^2 \right)^{1/2}$$  but it's not useful here. Is my expansion of the state $| x \rangle$ correct? Why do I get (author?) when I use \citet with natbib? I would like to show the author names using \citet but I get just the reference number. Here is a minimal code:  \documentclass{report} \usepackage[utf8]{inputenc} \usepackage[english]{babel} \usepackage{natbib}  \begin{document}   The author \citet{toschi09} has shown that ..  \bibliographystyle{plain} \bibliography{foo}  \end{document}   And here is foo.bib  @article{toschi09, author = {Toschi, F. and Bodenschatz, E.}, title = {Lagrangian Properties of Particles in Turbulence}, journal = {Annual Review of Fluid Mechanics}, volume = {41}, number = {1}, pages = {375-404}, year = {2009},  }   What I get is:     The author (author?) [1] has shown that ..   Any help will be more than welcome, thank you! Unit testing a method that calls another method How to completely delete the head of a function expression How can we recover the Newtonian gravitational potential from the metric of general relativity? Basically on my site I have a bunch of song lyrics and in a static page I want to show them listed by album  and album position of the song and I have two custom fields with that data, sd_album_title and `sd_album_track_n. Plus some of the songs don't have an album yet, so both values are void, and I wish to list those ones at the foot of the others, sorted by alphabetical order.  The latest thing I tried at least to sort everything by the two field is this one:  $key = 'sd_album_title'; $themeta = get_post_meta($post-&gt;ID, $key, TRUE);  add_filter( 'pre_get_posts', 'my_get_posts' ); function my_get_posts( $query ) {     if ($themeta != '') {         $query-&gt;set( 'post_type', 'lyric' );         $query-&gt;set( 'meta_key', 'sd_album_title' );         $query-&gt;set( 'orderby', 'meta_value' );         $query-&gt;set( 'order', 'ASC' );         $query-&gt;set( 'meta_query', array(               array(                     'key' =&gt; 'sd_album_title'               ),               array(                     'key' =&gt; 'sd_album_track_n',                     'value' =&gt; 'target_value',                     'compare' =&gt; '&gt;=',                     'type' =&gt; 'numeric'               )         ));     }     return $query; }  $getlist= 'my_get_posts'; $posts = get_posts( $getlist );   And my intention was to put an else at the end of it with an array ordered by title for the other songs, but it returns nothing as it is. Could something like this work with some corrections or am I on a totally wrong path? Is there a quick way to reset a .blend files windows and settings to default Whenever I download a .blend from someone all of the windows and settings are the way they have left them as it is saved in the file. It takes way to long to rearrange every window and toolbar to the way it is by default. Is there any tool or shortcut that can reset the UI to blenders default and just leave the actual contents of the file? The only way I could do this is by creating a new file and using link/append but this is not the best option. Viber notification is not in the right position Professionals: Would you choose GIMP over Photoshop and/or Inkscape over Illustrator? We know that the maximum level a dweller can train to on any SPECIAL skill is 10, however this does not consider bonuses given from their outfit.    Is there any additional benefit for going over 10? For example, a dweller with an Intelligence skill of 10 wearing a lab coat that boosts Intelligence by 3?   If it is a hard cap, would it be more useful to use outfits that raise a secondary characteristic instead? Clear 301-redirect cache in Firefox Is it possible to clear only 301-redirects from Firefox's cache? CTRL+F5 doesn't do the job since you just reload the target without caching but do not clear the cached redirect.  An option to disable caching of those redirects completely would be fine, too - but some way (possibly through an extension) to remove those cached redirects would be better.  Note: I'm not looking for answers that disable all caching (including CSS, JS, etc.) Suppose I've just made the switch to . I have chosen one of the built-in styles (numeric, alphabetic, authoryear, authortitle, verbose) or of the custom styles available at CTAN, and I've figured out how to sort/compress citations. The bibliography and the in-text-citations look approximately like I want, but need to be tweaked. I've taken a look at the biblatex documentation for advice, but it is somewhat daunting. How do I get started? To add some focus, customization in the following areas would come in handy:   Suppressing of specific BibTeX fields (e.g., publisher); Formatting of fields for specific entry types (e.g., titles of articles not inside quotation marks); Formatting of citation postnotes (i.e., getting rid of "p."/"pp."); Spacing and punctuation in the bibliography (e.g., commas instead of periods as unit separators); Order of first names and last names of authors/editors in the bibliography; Order of certain fields in the bibliography (e.g., swapping location and publisher); Language-specific terms (e.g., replacing "References" with "Works Cited").   Finally, assuming that I'll want to use my style adjustments in a multitude of documents: Where do I put the relevant macro stuff?