Sometimes I have a mathematical formula using, e.g.,  \dot{x} in a footnote but I have difficulties in recognizing the effective presence of a dotted variable (my fault, I know... to quote the poet "That's not the electric light, my friend\\That's your vision growing dim.").  Anyway, is it possible to use a heavier symbol for the dot that is usually used to indicate derivation w.r.t. time when used in a footnote?
I'm writing up some notes that will be displayed on an overhead projector. The standard time-derivative \dot{x} produces a dot that is hard to see. Does anyone know of a package or have a macro that produces a (nice looking) larger dot? Similarly with \ddot{x}.  At the moment, I've been supplied with some ugly code that produces an ugly output:  \def\dt#1{{\buildrel  {\hbox{\LARGE . }} \over {#1}}}    % dot-over  \def\ddt#1{{\buildrel {\hbox{\LARGE ..}} \over {#1}}}    % double dot
Checking the maximality of a principal ideal in $R[x]$ Let $R = \mathbb{Z}_{(2)}$ be the localization of $\mathbb{Z}$ at the prime ideal generated by $2$ in $\mathbb{Z}$. Then prove that the ideal generated by $(2x-1)$ is maximal in $R[x]$. How to use xcolor to color a pgfplot How do I use xcolor to color a specific cell from a table in pgfplots? Is xcolor the best tool to use here? I'm trying to loop over a list of colors and color the cells in the column individually.  \documentclass{article} \usepackage{pgfplotstable,filecontents} \RequirePackage{listofitems} \usepackage{}  \begin{filecontents*}{test.csv}     ColA, ColB, ColC     0.17, 0.91, 0.67     0.15, 0.17, 0.92     0.48, 0.1, 0.28 \end{filecontents*}     \begin{document}     \pgfplotstabletypeset[col sep=comma,     ]{test.csv}     \def\mylistOne{green, blue, orange}     \readlist*\mylistTwo{\mylistOne}     \newcounter{myCounter}     \setcounter{myCounter}{-1}     \foreachitem\x\in\mylistTwo[]{         \stepcounter{myCounter}         \pgfplotstableset{             every row \themyCounter column 1/.style={                 \cellcolor{\x}         }     } } \end{document} Introduction to proofs with a fair amount of hand-holding? Lately I've gotten a friend of mine interested in mathematics. He has no college-level education to speak of, but is well employed as a software engineer. So I feel he's competent to learn this stuff on his own.  He asked me recently if there was a 'mathematical' version of .  The point being, if there was an "introduction to proofs" book which took a more hand-holding approach. He's also expressed fondness for the .  However, metamath's proofs are obviously a bit too low level to learn anything serious.  At one point in our conversation, I mentioned the dependently typed programming language , but I felt it's not quite as helpful until he at least gets some experience with  (for which the target audience of Agda is Haskell programmers, hence the similarity in syntax).  Anyone have any good suggestions on a book? Using "you" and "your" as a representation for yourself and everyone in general Example sentence:     I love when your dog just lets you sit there to pet them. You don’t necessarily know if they are enjoying it, but they love you enough to just sit there with you for a bit.   Is this correct? We assume the words "you" and "your" refer to the speaker of the sentence, and not to the listener, as second-person usually does. But it also refers to dog owners in general. I have always been curious about this. Tikzcd conflict with babel and cd I have this problem: when I try to compile a diagram I get the following message:     I think the culprit is a tikzcd arrow in ell 1-1   But I have not problem when, in the tikzlibrary, I just use cd, matrix and backgrounds. The problem is when using babel and cd at the same time.  \documentclass{article} \usepackage{amsfonts,amssymb,amsmath,tikz} \usepackage[spanish]{babel} \usepackage[latin1]{inputenc} \usepackage[mathcal]{euscript}  \usetikzlibrary{babel,cd,matrix,backgrounds}  \begin{document} \begin{center}   \begin{tikzcd}     X\rar[mapsto]{T}&amp;Y   \end{tikzcd} \end{center}  \end{document} Frequency count of two column in R What happens if I use RAM of a faster speed than the CPU supports? What are the benefits of nickel-plated chains? Bicycle chains with higher model numbers (and slightly higher prices) are often nickel-plated or half-nickel-plated. What are the benefits of nickel-plated chains over non-nickel-plated chains?  How durable is the plating--does it wear off, or do its benefits last for the life of the chain? The definite article implying the generic idea of something I know that the definite article "the" can be used to mean a generic idea of something as in "the lion is the king of the animals." In this sentence, the in "the lion" is used to imply the general image of lions, so not specifying a particular lion.   However, I am confused in identifying where a "the" in a sentence is used for a general idea or a specific reference. For example, in the sentence "the price of gas is soaring", I heard that "the" in the sentence is an example of the generic use of the. Although I can easily understand the generic use of "the" in the lion example, but I do not understand how there is an general idea about gas price. Soaring gas price is something real,and gas prices in different regions( in a hypothetical situation) can be different. So, if I say "the price of gas is soaring", do I mean the price of gas that is determined by the world's oil system or can I say "the gas price" even when I am indicating the state of gas price in "a particular region"?    I know it is even difficult to understand my question, but I hope someone could find what I am confused about and give an answer. How to compute $\prod\limits^{\infty}_{n=2} \frac{n^3-1}{n^3+1}$ Package pgfplots Error: CRITICAL: shader=interp: got unsupported pdf shading type '0' For the set of data , the following code can't compile showing the error     Package pgfplots Error: CRITICAL: shader=interp: got unsupported pdf   shading type '0'. This may corrupt your pdf!.   \documentclass[border= 5mm]{standalone} \usepackage{pgfplots} \pgfplotsset{compat=newest} \begin{document}     \begin{tikzpicture}     \begin{axis}[unbounded coords=jump, view={70}{40}]     \addplot3 [surf,shader=interp]      table [x index={0}, y index={1}, col sep=tab] {mySurfaceData.txt};     \end{axis}     \end{tikzpicture} \end{document}    So, what went wrong to cause this?  P.S. the original data without NaN is available , where I would like to skip plotting those points of z=1. Can someone explain collection_select to me in clear, simple terms? I wonder which of the two is correct:        I have a red and a blue car.   I have a red and a blue cars.      or        Everyone has a left and a right arms.   Everyone has a left and a right arm.      My (non-native) inclination would be for option 1, as it sounds better.  On the other hand, in the following examples, the plural sounds better to me.    Everyone has left and right arms. I have old and new cars. (when I only have only one old car and one new car) The left and the right arms are...   But are they correct? What's the limit of the sequence $\lim\limits_{n \to\infty} \frac{n!}{n^n}$? Convergence of $\int_0^\infty $sin$ (x^p) dx$ Interaction with the site on the app should count towards Enthusiast/Fanatic If I do any of the below, which would normally constitute "activity" on any Stack Exchange site (including mobile):   View my profile Vote on any question or comment Visit one or more questions   ...then Stack Exchange considers me to have "visited" the site.  If I do any of the below on the mobile app:   Vote on any question or comment Visit one or more questions   ...then Stack Exchange does not consider me to have visited the site.  If one wants the app to have feature parity with the mobile site, then shouldn't my participation within the app also count towards the Enthusiast/Fanatic badge? Before I met her I had a poor opinion of her.   As person had a poor opinion before a particular time in past (before He met her) so I think there should be had had.   There are some more example like this:   Before I went to the university, I worked/had worked as a carpenter for 5 years. Before I opened the door, I put/had put the key in the lock. Before I opened the door, I looked/had looked carefully into the barn for snipers.   In all these sentence, for me, it should be perfect tense.  I asked that question on another platform where I was told that if sequence of past event is obvious and sentences uses "before"and "after", we often use past tense. Which means we should use past tense in all these sentences. But I have another sentence "The train had left before I reached the station." If I follow above mentioned rule there should be "left" instead of "had left". But I am damn sure this sentence is correct with "had left".   Am I correct?  Thank you creating a diagonal matrix with a variable amount of parameters I have a Toshiba Satellite laptop. My charger has stopped working.  I have access to a Lenovo charger. Can I use this charger on my laptop? I am trying to get a better feel for the topology of ordinals and just received a great answer to this  where the Cantor-Bendixson rank and degree turn out to be a complete homeomorphism invariant of countable compact spaces. Now I am curious about what is going on within homeomorphism classes of ordinals. In particular, I want to know how to characterize countable ordinals $\alpha$ which are minimal among all ordinals homeomorphic to $\alpha$.   Certainly finite ordinals and $\omega$ are easy. Next, if $\alpha\cong \omega+1$, then it seems like we would have to have $\omega+1\leq \alpha&lt;\omega +\omega$ since there can only be one limit point in $\alpha$. Things become a little fuzzier for me with ordinals that have infinitely many limit points.  For instance, suppose $\alpha$ is an ordinal homeomorphic to $\omega^{\omega}$. Is it necessarily true that $\alpha\geq \omega^{\omega}$? Is there a general rule for knowing when an ordinal is the smallest among all ordinals homeomorphic to it?