I remember hearing an interesting theory once, I don't know the source. Since there are some numbers that are precisely expressible in decimal notation that repeat in a binary base, and vice versa, perhaps there exists a base in which irrational numbers are rational.  The more I think about it, the less likely this seems, and my guess is that whatever proof that $\pi$ or $e$ are irrational doesn't involve the decimal base notation. But perhaps there's some research into this?
I am from a physics background and my mathematics is not very good, so pardon my insolence with the question.  Editing based on the comments : We know that $\pi$ in decimal (i.e. base 10) is transcendental. Is it possible to have a radix base in which $\pi$ can be rational in that base ?  PS : My question is in general for any transcendental number.
C++ inlining class methods causes undefined reference What info does Google backup? Does anyone know what exactly does Google backup (and restore) when you enable that option?  Also, are we able to see this list somewhere? (Maybe hidden n-levels deep in Google Account information?)  Reason I ask is I've had the unfortunate experience of my SD Card dying on me, put in a temporary SD Card and allowed Google to do the auto-restore.  Some things that were restored:   Saved wireless networks Background Some apps - strangely enough only a subset of my apps were restored (some with data, some without). All previous apps were installed via Android Market.   Then finally got my new SD Card, put that in and the following were restored   Saved wireless networks Some apps - again, same problem... only a subset (different subset, even fewer apps). This time no data seemed to have been restored either.   I think it would be very helpful to be able to view/manage a list of what is backed up, and thus would be restored (but I have yet to find this list... if it even exists). Is it okay to vectorize this image to make a poster out of it even though the image is not Creative Commons or anything like that? I'm not using any part of the image directly and only going to use it as a guide to make my own SVG version.  This is the image:    Here is .  It says that it is CC licensed but the original NatGeo one isn't, I don't think.  I don't plan to make money off it or anything, I just want a nice poster and the quality of the original isn't that good. I forgot the passcode for my iPad restrictions. How can I disable them? Gauss's Lemma for polynomials claims that a non-constant polynomial in $\mathbb{Z}[X]$ is irreducible in $\mathbb{Z}[X]$ if and only if it is both irreducible in $\mathbb{Q}[X]$ and primitive in $\mathbb{Z}[X]$.   I wonder if this holds for multivariable case.      Is it true that a non-constant polynomial in $\mathbb{Z}[X_1,\dots,X_n]$ is irreducible in $\mathbb{Z}[X_1,\dots,X_n]$ if and only if it is both irreducible in $\mathbb{Q}[X_1,\dots,X_n]$ and primitive in $\mathbb{Z}[X_1,\dots,X_n]$?    Thank you for your help. I have defined my own language whose syntax is very close to the one of Pascal. I would like to type the following program for instance. Many people use the packages algorithmicx or algorithm2e to print programs, but it seems that we have to use their specific keywords of its syntax like procedure, end while.  I just want to indent spaces when needed, and bold some words when I want (sorry that I could not bold letters in the following figure). Do I have to use  texttt for each line? Also, with verbatim, I could not bold words...  Also, as the program is not large, I would need to put it on the left side of the page, and leave space for some explanasion text on its right hand side. So I  guss I need to get them all together, and use multicols.  Could anyone help?  program test                                      some text here var   i : integer;                                    ...    b : boolean; begin    i := 1;                                        ...    b := true;    while i &lt; 15 do       i := i  + 1;       b := not b                                  some text here    od end   Edit1: Following @Werner's tabbing solution, I have made the code a minipage:  \begin{minipage}[t]{0.48\linewidth}% \begin{tabbing} Werner's solution \end{tabbing} \end{minipage}\hfill \begin{minipage}[t]{0.48\linewidth} a paragraph \end{minipage}   Actually as the code shows, I want the texts to be another separated minipage on the right hand side of the code. I have then 2 questions:   is it reasonable to make 0.48\linewidth instead of 0.5\linewidth? 0.48\linewidth is a conventional choice? is it possible to make a frame around the code, and use \caption and \label to make it a reference (I prefer figures)? Intuition behind the definition of a measurable set How to avoid procrastination during the research phase of my PhD? How to solve this probability problem analytically (instead of using simulation)? Probability of Bill wins the game if he goes first How do I add a directory to the $PATH in Ubuntu and make the changes permanent? Algorithms for automatic model selection GCD of rationals Disclaimer: I'm an engineer, not a mathematician  Somebody claimed that $\gcd$ only is applicable for integers, but it seems I'm perfectly able to apply it to rationals also:    $$ \gcd\left(\frac{13}{6}, \frac{3}{4} \right) = \frac{1}{12} $$  I can do this for a number of cases on sight, but I need a method. I tried Euclid's algorithm, but I'm not sure about the end condition: a remainder of 0 doesn't seem to work here.    So I tried the following:    $$\gcd\left(\frac{a}{b}, \frac{c}{d} \right) = \frac{\gcd(a\cdot d, c \cdot b)}{b \cdot d}$$  This seems to work, but I'm just following my intuition, and I would like to know if this is a valid equation, maybe the correct method. (It is in any case consistent with $\gcd$ over the natural numbers.)  I'm not a mathematician, so please type slowly :-) Can you grammatically end a sentence with "with"? Do you want to come with? Can I come with?  I seem to hear this construction more often in recent years, but it still grates on my ear. I know it's often said that one shouldn't , but I class that rule along with  (i.e. — pedantic tosh). Is it always informal/casual speech to end a sentence with &quot;with&quot;? Was it ever thus? Will everything eventually be a single black hole? Given the idea that gravity is always a factor (even though greater distances are excessively tiny), would everything eventually end up forming a single black hole?  My thinking is that, with infinite time, all mass will eventually be pulled together. "It is they who lied" or "it is them who lied?" Which is the correct usage of the third person, plural pronoun?     It is they who lied.   It is them who lied. Hide deleted answers with certain characteristics Today I exceeded 10K reputation on Stack Overflow, and I see deleted answers.  I am now faced with pages like  where half the answers are "deleted."    Among these are many non-answers deleted by diamond moderators, and a self-deleted answer deleted on Nov 25 '09.  I find this very distracting, especially in my chosen sort order of "oldest" where these deleted answers are NOT displayed at the bottom.  I wish to be able to hide deleted answers based on combinations of characteristics such as:   age since deletion deleted-by-owner deleted by diamond moderators zero undelete votes   This would be a setting every user could enable for himself.    Here are HTML excerpts that may be useful for userscript filtering.  This shows the code that appears for a moderator deletion, as well as the date stamp.  &lt;div class="deleted-answer-info"&gt;deleted by &lt;a href="/users/10936/dori"&gt;Dori&lt;/a&gt;&lt;span class="mod-flair" title="moderator"&gt;♦&lt;/span&gt; &lt;span title="2011-06-26 09:13:34Z" class="relativetime"&gt;Jun 26 at 9:13&lt;/span&gt;&lt;/div&gt;   Here is the same class for deleted by owner:  &lt;div class="deleted-answer-info"&gt;deleted by owner &lt;span title="2009-11-25 19:12:11Z" class="relativetime"&gt;Nov 25 '09 at 19:12&lt;/span&gt;&lt;/div&gt; Is it possible to have a 100% secure virtual private server? How would I import/export Blender's preferences? I constantly stay up to date with each new release of Blender, but this means my preferences are wiped clean each time. How do I export/import these preferences to avoid loosing my carefully crafted set up each time? One of my players has a +1 shortbow, and recently found some +1 arrows. If he fires a +1 arrow from a +1 bow, will the bonus to attack and damage be +1, or +2? I have two exchange accounts on my iPhone 4. One that connects to my gmail, the other connects to my work's Lotus Notes. There are no overlapping contacts in the two accounts. There are also no contacts saved locally on my phone.   When I enable contacts in both accounts, I get two identical entries for each of the contacts in my gmail. If I disable the Notes exchange account, then there are no more duplicates. If I have Notes contacts enabled, and gmail contacts disabled then I have no contacts at all.  Does anyone know what is going on? Is this a problem with having multiple exchange accounts or is it a Lotus Traveler problem? (I tend to blame Notes for all the trouble in the world, but that is just my bias)  Thanks all.