Pi is infinite, but not random. 1/3rd for example is certain not to contain a 4, but i found my full birthday in Pi. Is there proof that every conceivable combination of numbers, such as all Natural numbers in order? I'm having a hard time imagining how all natural numbers could have something before and after them though so can it be proven that every finite numbercombination is found in Pi, such as every birthday of every person in chronological order and everyones creditcard pin and then some. Or is it likely/unlikely/impossible(or impossible to tell)? I'm asking out of my own curiosity.
I came across the :    Which states:     $\pi$ Pi      Pi is an infinite, nonrepeating $($sic$)$ decimal - meaning that   every possible number combination exists somewhere in pi.  Converted   into ASCII text, somewhere in that infinite string of digits is the   name of every person you will ever love, the date, time and manner    of your death, and the answers to all the great questions of    the universe.   Is this true? Does it make any sense ?
A friend of mine asked me the following question:      Suppose you have a basket in which there is a coin. The coin is marked   with the number one. At noon less one minute, someone takes the coin   number one and put into the basket two coins: the number two and the   number three. At noon less $\frac{1}{2}$ minute, he takes the coin   number two and put into the basket the coins number $4$ and the number   $5$ and so on. At noon less $\frac{1}{k}$ he takes the coin number $k$   and put two other coins.       The question is: How many coins I can find in the basket at noon?   Intuitively the answer is $\infty$ because I added one coin for infinite times. But the correct answer seems to be $0$ because every coin numbered $k$ has been removed at noon less $\frac{1}{k}$ of minute. What is the correct answer? Thanks. While drawing a simple 3D (fake 3D in fact) cube, I realized that the corners end up with unwanted extensions of the line. I understand this is related to the width of the lines themselves, but how can I remove them? An alternative solution of drawing the desired figure is also welcomed.  Example:  \documentclass{article} \usepackage{tikz}   \begin{document} \begin{tikzpicture}  \draw[draw=black,fill=gray!20] (0,0) --(4.8,0)-- (4.8,5)--(0, 5)--cycle; \draw[draw=black,fill=gray!20] (4.8,5) -- (4.9,4.8)--(4.9,-0.1)--(4.8,0)--cycle; \draw[draw=black,fill=gray!20] (0,0) -- (0.1,-0.1)--(4.9,-0.1)--(4.8,0)--cycle; \draw[dashed,draw=black] (4.8,5) -- (4.9,4.8)--(0.1,4.8)--(0.,5)--cycle; \draw[dashed,draw=black] (0.1,-0.1)--(0.1,4.8)--(0.,5)--(0,0)--cycle; \end{tikzpicture} \end{document} Horizontal spacing issue in \listoftheorems using amsthm + thmtools Irreducibility of a polynomial if it has no root (Capelli) Let $F$ be a field of arbitrary characteristic, $a\in F$, and $p$ a prime number. Show that $$f(X)=X^p-a$$ is irreducible in $F[X]$ if it has no root in $F$.   This  to a related question mentions the result is due to Capelli.  I can prove the result if $F$ has characteristic $p$ as follows.  Suppose $f$ is reducible: $f(X)=g(X)h(X)$ with $g(X)$ an irreducible factor of degree $m$, $1\le m&lt;p$. Then if $\alpha$ is a root of $g$ in some extension field $K$ of $F$, we have $$f(X)=X^p-\alpha^p=(X-\alpha)^p$$ so its divisor $g(X)$ must be of the form $(X-\alpha)^m$. Since the coefficient of $X^{m-1}$ in $g$ is in $F$, we have $m\alpha\in F$.  So $\alpha\in F$ because $m$ is invertible modulo $p$.  How would you show the result in other characteristics? How do I preview tag wiki exerpt? How do I put a link there? I've edited  to include a link into exerpt. But it shows Markdown source of the link instead of actual link.   How do I preview the exerpt while editing it? Where to find syntax and available Markdown features in exerpts? How do I include the link properly? Moving from HTTP to HTTPS in Google Search Console How does the tester screwdriver work? How does the tester screwdriver work? If I put the tester screwdriver inside the "hot wire" of an electrical socket, it lits up if I press my finger against the metal cap on top of the screwdriver. This happens also if I stand on a surface of isolating material, such as wood. I read elsewhere that this happens due to stray capacitance formed by the "hot wire", the human body, and the ground. One has  $$ Z = R + \dfrac{1}{j \omega C}  $$  for the impedance, so if C  is high enough, the impedance should be close to r , the "effective resistance" of the formed circuit. Here I get lost; why r  is small enough to cause a current in the range of mA  even if I stand on an isolating surface?  So really what I am asking is how one may represent the system hot wire - screwdriver - human body - wooden floor - building - ground as an electrical circuit, and which parts of the physical system contribute to the resistance, capacitance (and inductance?) and in which proportion, even very approximately. Italic citation reference for author name using natbib Explain why $\mathbb{Z \times Z}$ and $\mathbb{R \times R}$ is not a field How can I check if the Active Object has a specific modifier so that when I run my code, it doesn't add the modifier again to the object? It should add the modifier only to the object which does not use that modifier. The Winter Bash is back and the hats are listed below.  As always, there are only two answers: one for the secret hats, and one for the regular hats. The secret hat list will be updated as we learn them.  Only edit the secret hat answer with definitive and correct triggers. This is not the place to post guesses.    If you'd like to discuss Winter Bash, hats or just have a question about the WB please come over to the .  Please keep the comments here clean. As always comments are not meant for discussion, conversation, "I just got hat X", etc use the  for that (the remaining meta mods will periodically clean the comments). I know you are excited you just got a secret hat, but please instead of posting a comment come over to the  and tell us all there.  Provided that "It's important to know your history... in more ways than one"  again this year, here are the hats from prior years: Changing text applied when duplicating file in Finder When duplicating files in the finder, OS X attaches a space followed by 'copy' to the file name. This can lead to some file alphabetizing problems and the copies may appear out of order (not directly subsequent to the original). Is there a way to change the appended text? I would prefer that it says '_1' or _copy. Thanks. How to create a bootable USB with multiple ISO images in it What I want is to create a bootable pen drive that shows GRUB menu and I can select any of the several bootable systems from there to install/run. I have several ISO images that I want to install in the USB like Ubuntu, Fedora, System Rescue CD, Windows XP and Windows 7 (The windows versions are optional, mostly am looking for a multi installer for Linux distros, specially Ubuntu version)  The default Startup Disk Creator only works with Linux Images and only 1 at a time (At least for the mean time. If it allows more systems and multiple ISOs it would be awesome)  What method exists that I can use step by step to create a bootable USB Drive with multiple images than can be booted from the USB and selected from GRUB. It must support Windows Images and Linux Images.  Alternatively, is there also a way to have multiple versions of the Ubuntu installation ISO on same USB Drive, such as, when booting from it, I get to choose what Ubuntu version and architecture to install, for example:     BOOT MENU   Ubuntu 12.04 32 Bit   Ubuntu 12.04 64 Bit   Ubuntu 12.10 32 Bit   Ubuntu 12.10 64 Bit   UPDATE: Wanted to add that the English version for the post mentioned by daithib8 is here: Why does water pouring from a glass sometimes travel down the side of the glass? Remove marker using lat or long gmaps v3 How can I include custom post types on a tag page? I'm using custom post types, but they don't appear on tag pages along with regular posts and i'd like to include both standard and custom post types on tag or category pages. What would be required before the loop to include all posts? (including custom type). Updated: To add, I found this code , which worked perfectly for the first part: add_filter('pre_get_posts', 'query_post_type'); function query_post_type($query) {   if ( is_category() || is_tag() &amp;&amp; empty( $query-&gt;query_vars['suppress_filters'] ) ) {     $post_type = get_query_var('post_type');     if($post_type)         $post_type = $post_type;     else         $post_type = array('post','cpt'); // replace cpt to your custom post type     $query-&gt;set('post_type',$post_type);     return $query;     } }  Second question still remains though: Is there a way to allow readers to filter by post type? So either of the following would work..  example.com/tag/blue?post_type=custom example.com/tag/blue?post_type=post What do you wish someone had told you before your first commute? Cannot locate Ubuntu Software Center via Firefox to open APT links I'm trying to locate where the Ubuntu Software Center is to choose as default for handling APT links in Firefox.  I can click on the links, and I get the pop-up, but Ubuntu Software Center is not there.  I tried to choose an application through Firefox's settings and through the pop-up, but I don't know the path.  As you can see by my screen shot for the pop-up I chose the wrong one as that doesn't work.  What is the correct path I need to select the correct file?  EDIT - I added a fourth screen shot.  I don't have it in that location.  This is what I have.  My view is in ABC order, and it's showing hidden files. Implied string comparison, 0=='', but 1=='1' How can I explain to people that the phrase “off of ” is grammatically incorrect?