I'm using amsmath and amsfonts to typeset my homework, and since it will be read on a screen, I would like to make \tag{comments inside equations} differently colored, and optimally downsize them by a few points.   While I could put \color and font instructions in every \tag instance, I've got them scattered all over the place and would like a unified way to change it globally. I have figured out how to use the sectsty package to color all section fonts to make them stand out on-screen slightly, is there a similar method for amsmath's align environment and tags?  Forgive my extreme TeX ignorance. Also forgive my math ignorance... here's some sample stuff:  \begin{align*} A &amp;= B \\ &amp;= \frac{B}{\text{sometimes the equation gets really long so the tag goes on the next line}} \tag{Here is where I say something stupid} \\ &amp;= \frac{1}{0} = \infty \tag{Tags often include math, like $\frac{\sin \theta}{\theta}$} \end{align*}
I'm new to LaTeX and I'm trying to figure out how to correctly format a proof. Can someone show me a basic template for how to do this?   The part I am having the most trouble with is creating new columns and customizing alignment... for instance, how do I add a right-aligned annotation (i.e. by distributive property) to a line of this sample proof? Should I use eqnarray* or is there a better option?  \begin{proof}   Let $t,u \in \mathbb{R}$ where $t=xy$ and $u=zw$. So,   \begin{eqnarray*}     4xyzw &amp;=&amp; 2\cdot2tu \\     &amp;\le&amp; 2\cdot(t^2+u^2) \\     &amp;=&amp; 2\cdot((xy)^2+(zw)^2) \\     &amp;=&amp; 2\cdot(x^2y^2+z^2w^2) \\     &amp;=&amp; 2x^2y^2+2z^2w^2 \\     &amp;\le&amp; ((x^2)^2+(y^2)^2)+((z^2)^2)+(w^2)^2) \\     &amp;=&amp; x^4+y^4+z^4+w^4   \end{eqnarray*} \end{proof}
Polynomial in $n$ variables Let $f$ be polynomial in $n$ variables. If we have $f(a_1,\ldots,a_n) = 0, a_i \in S_i$ and $S_1,\ldots,S_n$ are infinite subsets of a field $k$, how can I show that $f=0$? Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal Let I and J be ideals of a ring R. Show by example that the set of products {xy | x ∈ I, y ∈ J} need not be an ideal, but that the set of finite sums of products of elements of I and J is an ideal. This ideal is called the product ideal, and is denoted by IJ.   I want to check if my work on the first part makes any sense. I am not sure if I am picking the right example.  If I let R = Z and I = (2) and J = (3) then I has multiples of 2, and J has multiples of 3  6 will divide the product IJ if we add 2 and 3 though we get 5 in IJ, but I am not sure if 5 Divides IJ. Calculate: $$\int_{0}^{2\pi}e^{R{ {\cos t}}}\cos(R\sin t+3t)\mathrm{d}t$$ My try: $\displaystyle\int_{0}^{2\pi}e^{R{ {\cos t}}}\cos(R\sin t+3t)dt\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\cos(\mathfrak{I\textrm{z}}+3(-i\log z)dz\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\mathfrak{R\textrm{e}}^{(\mathfrak{I\textrm{z}}+3(-i\log z))i}dz\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\mathfrak{R\textrm{e}^{\mathfrak{I\textrm{z}}}}z^{3}dz\\ \displaystyle \int_{|z|=R}e^{\mathfrak{R\textrm{z}}}\mathfrak{R\textrm{e}^{\mathfrak{I\textrm{z}}}R}z^{3}dz$ and there is nothing here that is not holomorphic, therefore according to Cauchy theorem it must be exactly $0$. How do I check the integrity of a storage medium (hard disk or flash drive)? I've run across (personally or by proxy) a bunch of storage media that exhibited physical problems during their life. Hard disks, solid state drives and other flash storage media all fail after some time. The situation is worse with USB flash drives and flash cards because of the large amount of suppliers with inferior flash cell and flash controller quality.  How can I reliably detect if a storage drive suffers from physical damage?  Note that this question isn't about file system integrity (which can be checked with ). Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix How to open a web page from my application? I want to make my WPF application open the default browser and go to a certain web page.  How do I do that? $K \subset \mathbb{R}^n$ is compact iff it is closed and bounded I want to prove $\Leftarrow$.  I just need one more step, now. If I find a compact set that contains K, then it will finish the proof. Rudin take a k-cell to do that, but before it he proves that every k-cell is compact, and I think I can take a more simple compact to do this step. I has thinked in the closed ball, but don't know how to prove that it is compact. Can anyone help me to find this set, if it really exists? Thanks. What size canvas should logos be designed on? When designing a logo is there a minimum size canvas that should be used to keep quality when it is enlarged or when reduced?  Obviously the dimensions of a canvas depend on the shape of the logo, but is there a sugested size? Why can I no longer easily navigate inside of this mesh? Mail.app crashes constantly, even after deleting mail profile and cache MySQL single table static and dynamic pivot I have a table that looks like this:  +----------------------------------------+ |Name                | kode      | jum   | +----------------------------------------+ | aman               |kode1      | 2     | | aman               |kode2      | 1     | | jhon               |kode1      | 4     | | amir               |kode2      | 4     | +--------------------+-----------+-------+   How can I make a view like this with MySQL?                      kode1    kode2     count aman                  2         1        3   jhon                  0         4        4 amir                  0         4        4 This is probably a silly question, but how can I run ANOVA using only the mean, standard deviation, and the sample size?  i.e.  Group  mean    sd    n  1:    200      5    5    2:    100     22    5  3:    150     14    5   I am using Statsoft Statistica software.  I know how to run it using the spreadsheet with all the data, but I have never done this using only the information listed above.  Any information would be greatly appreciated. Number of solutions to the congruence $x^q \equiv 1 \mod p$. Let $p, q$ be distinct odd primes, I would like to compute the number of solution $\mod p$ to the congruence $x^q \equiv 1 \mod p$. (Show that it's $gcd(q, p - 1))$  If $x^q \equiv 1 \mod p$, since $q$ is prime, this must mean that $x$ is either $1$ or has order $q$.   Hence, the problem reduces to finding the number of elements of $U_p$ which is either $1$ or has order $q$.  If $ q \nmid  p - 1$, then there is only one element, namely $1$.  If $q \mid p - 1$, then the number of elements of order $q$ is $\phi(q) = q - 1$, and so the number of solutions to the congruence $\mod p$ is $q - 1 + 1 = q$, and in either case the number of solutions is $\gcd(q, p - 1)$.  Does this look fine? Formal Proof that area of a rectangle is $ab$ I tried to prove that the area of a rectangle is $ab$ given side lengths $a$ and $b$.  The best I can do is the assume the area of a $1\times1$ square is $1$. Then not the number of $1\times1$ squares that fit in an $a\times b$ rectangle is $ab$. Therefore area is $a\cdot b$. This does not seem rigorous however. How to fix "Package is in a very bad inconsistent state" error? I can't update my system because it freezes while installing a third-party update (zramswap-enabler)! Sometimes I get the following message in Update manager:  Could not initialize the package information An unresolvable problem occurred while initializing the package information. Please report this bug against the 'update-manager' package and include the following error message: E:The package zramswap-enabler needs to be reinstalled, but I can't find an archive for it.  I tried to remove the zramswap-enabler, but it's impossible because I get the following message: dpkg: error processing zramswap-enabler (--remove):  Package is in a very bad inconsistent state - you should  reinstall it before attempting a removal. Errors were encountered while processing:  zramswap-enabler E: Sub-process /usr/bin/dpkg returned an error code (1)  Actually I would really reinstall that package, but it is unable to do it! If I remove this third-party PPA then the system is warning me about a very very serious problem. So why can I not install/reinstall/remove/update this package and why freezes the updater if I try to update? View history of changes Possible Duplicate:          How do I view the changes made to a question, in the SO-style visual diff?  I'm sure I've seen this before, but the "history" button eludes me. Clicking "edit" gives me a drop down of the revisions, but not the actual diff.    Edit  This edit is a demonstration of the revision history functionality. How to fix sculpting ridges? I ran into a problem I have never seen before and that is when I try to sculpt on a mesh, it sculpts like this:  Instead of this: I am using dyntopo with these settings:   I feel like theres a very obvious solution to this, but I have no idea what it is. Random place change in row with restrictions How could I randomly change places of characters in a text file, with some probability (say 10%)?  file:  1  34567 2  12356 3  16987   outcome:  1  35674 2  12653 3  61987 What is the exact difference between an autoregressive (AR) and vector autoregressive model (VAR)?  I always thought that VAR would just be for more than two variables, until I learned that AR can also have more than two variables. I.e. I had a misunderstanding(?) that AR models are not always bivariate.  Before I write too much potentially false assumptions about the difference between AR and VAR, it would rather be interested to see if anyone can make provide a quick and good summary. Deleting an element from an array in PHP