I am not sure because that element sign under the intersection sign is not aligned. Every time I use \bigcap, \limits, for instance,  $$N(G) = \bigcap \limits_{H\in \Sigma} N_G(H)$$.
70382
I have the following Latexcode:  \begin{equation} \mathscr{G} = A_{polygon} - \sum \limits_{C \in \Xi} A(C) \end{equation}   However, the sum index looks bad in my eyes, as the "is element of" sign is a little lower than the other two letters. It looks badly aligned.  Is there a way to fix this? I don't want to change to to smaller case letters as I have a convention for letter cases in my document.  edit: I've added a picture    I'd like the element sign to be above the red line i.e. vertically centered with C and Ξ.
123025
Can anyone help with this. I'm not sure at all what I'm doing wrong but i get an error Missing $ inserted.                   $ on the 2nd line with c)\  The rest of the text works fine and there are no $ signs that are not already paired in previous parts  \noindent c)\\ coordinates = (99,85),(190,220),(286,383)\\ \begin{align} error&amp;= \left | y-(a+bx) \right |\\ E&amp;= \left | y-(475.5+1.253x) \right |\\ (99,85): E&amp;=\left | 85-(475.5-1.253(99) \right |\\ &amp;=\left | 85-(351.5) \right |\\ &amp;=266.5\\ (190,220): E&amp;=\left | 220-(475.5-1.253(190) \right |\\ &amp;=\left | 220-(237.5) \right |\\ &amp;=17.5\\ (286,383): E&amp;=\left | 383-(475.5-1.253(286) \right |\\ &amp;=\left | 386-(117.2) \right |\\ &amp;=265.8\\ \end{align} $\therefore$ \text{Next location is "The Reservoir" at (190,220)} \end{document}
43077
This part C\frac{1}{\sqrt{G}}\sqrt{\rho} doesn't seem to be on the same height as this part \sqrt{b}\sqrt{l} when compiled. What am I doing wrong?  \begin{flalign*} T=C\frac{1}{\sqrt{G}}\sqrt{\rho}\sqrt{b}\sqrt{l} &amp;&amp; \end{flalign*}
31860
I would like to construct a formal proof of the following:  $$(A\setminus C)\setminus(B\setminus C) = (A\setminus B)\setminus C$$  Let $a∈A$ be an arbitrary element, we will show that $a\in A \cap \overline B \cap \overline C$.  For LHS, since $a\in A$, we have that $a\in (A \cap  \overline C) \cap  (\overline B \cap \overline C)$. This is equivalent to $a\in (A \cap  \overline B) \cap \overline C$.    For RHS, since $a\in A$, we have that $a\in (A \cap  \overline B) \cap \overline C$  $\therefore lhs \equiv rhs$ and this concludes the proof  I would be grateful for any feed back on this element chasing proof. Is it flawed or where should improvements be made?  Thanks
32353
I am having some difficulty getting this to display properly.      \begin{equation} {\bf H} = -{\bf \mu} \cdot {\bf B} = - \gamma B_o {\bf S}_z = -\frac{\gamma B_o\hbar}{2}  \begin{bmatrix} 1&amp;0\\0&amp;-1 \end{bmatrix}. \end{equation}   Which appears as,    I would like the matrix height to be consistant with the rest of the equation.
53312
I'm trying to prove that the rationals are not the countable intersection of open sets, but I still can't understand why   $$\bigcap_{n \in \mathbf{N}} \left\{\left(q - \frac 1n, q + \frac 1n\right) : q \in \mathbf{Q}\right\}$$   isn't a counter-example. Any ideas? Thanks!
79272
Please refer the attached image. I want to write \omega \in \mathbb{R} below sup as shown in the equation in the image. How should I do it?
27962
In the example below, an error is caused by \begin{align} and \end{align} but I do not see why:  \documentclass{book} \usepackage{amsmath} \newenvironment{subalign}{\begin{subequations}\begin{align}}{\end{align}\end{subequations}} \begin{document} \begin{subalign}      a&amp;=b\\     &amp;=b \end{subalign} \end{document}
38411
When i put the code $(f_{\mathcal{X}},f_{\mathcal{X}}^{\partial})$ I get the following:  But I want the subscripts to be aligned. How can I do this?
34577
When using \not together with wider symbols such as \Leftrightarrow the diagonal line produced by \not is placed too far to the left. How can the line be properly aligned? For example the following code \documentclass{article}  \begin{document}  \(\not\subset\)% Looks good  \(\not\approx\)% Looks good  \(\not\leftrightarrow\)% \not line is too far to the left  \(\not\Leftrightarrow\)% \not line is too far to the left  \end{document}  produces the following output where the last two symbols has got a misaligned diagonal line  Also, maybe the lines may need other changes than alignment to look good.
75226
\documentclass[11pt]{article} \usepackage{xfrac, array, tabu, multirow, graphicx, setspace, dcolumn, tikz} \usepackage[fleqn]{mathtools} %the argument for d specifies the maximum number of decimal places \usepackage[ngerman]{babel} \usepackage[applemac]{inputenc} \begin{document} \begin{align} \bar{x}&amp;=7+(2\times9) + (2\times10) + (4\times11) + (6\times12) + (7\times14)\\  &amp;+(2\times15) + (3\times16) + 17 + 18 + 19\\ \bar{x}&amp;=14  \end{align}  \end{document}   I was looking long and hard for an answer, I believe {alignat*} is capable to do what I want, I just can't figure out how. I want the too long equation to align as follows: 1st and 3rd row the = should be aligned. But I also want the 1st and 2nd row to be aligned where the first + comes in.
59750
I want some advice about how to format it better if I have to write a long text below a $\sum$ or a $\prod$ sign. Basically I want to explain the restriction over which the sum or the product is being taken.   For example how can I improve the looks of these equations,  $N_i (\rho) = \sum _ {B \in \rho s.t n_{\delta_j}(B) = 0    \forall j \neq i} n_{\delta_i} (B)$  $\sum _{ \rho s.t N_i(\rho) = a_i and M_i(\rho) = b_i}    \prod _{B \in \rho} \langle \prod_{i=1}^{n} \delta_i ^{n_{\delta_i}(B)}    y_i ^{n_{y_i}(B)} \rangle_c$
88581
So as I have learned from a previous post that the  \begin{aligned}... \end{aligned} with the usage of "&amp;" before "=" will help arrange neatly the equations where the equal sign of each equation will be just below the equal sign of the following equation and so on.  My question is if I have a total of 8 equations, how to number each equation and at the same time preserve the alignment of the equal signs.  Note if I use \begin{equation}... \end{equation}, I get only one number for the collection of 8 equations at the very end which is not what I want.
26817
\begin{multline*} \displaystyle \left \| f  \right \|_{M\dot{K}^{\alpha(\cdot),q}_{p(\cdot), \lambda}(\mathbb{R}^{n})} \approx \max \left\{ \sup_{L\leqslant0,L\in  \mathbb{Z}}2^{-L\lambda}\left ( \sum_{k=-\infty}^{L}2^{k\alpha(0)q}\left \|  f\chi_{k} \right \|^{q}_{L^{p(\cdot)}} \right )^{1/q},\\\sup_{L&gt;0,L\in \mathbb{Z}}\left[ 2^{-L\lambda}\left ( \sum_{k=-\infty}^{-1}2^{k\alpha(0)q} \left \| f\chi_{k} \right \|^{q}_{L^{p(\cdot)}} \right )^{1/q}\\ +2^{-L\lambda}\left ( \sum_{k=0}^{L}2^{k\alpha(\infty)q}\left \|  f\chi_{k} \right \|^{q}_{L^{p(\cdot)}} \right )^{1/q}\right] \right\}  \end{multline*}
98383
In the following piece of code  \begin{align*} [x \mapsto s]x &amp;= s \\ [x \mapsto s]y &amp;= y \qquad \text{als } y\neq x \\ [x \mapsto s](\la{y}t_1) &amp;= \la{y}[x \mapsto s]t_1 \qquad \text{als } y \neq x \text{ en   } y \not \in FV(s) \\ [x \mapsto s](t_1 \; t_2)&amp;= ([x \mapsto s]t_1)\;([x \mapsto s]t_2) \end{align*}   I am currently only aligning on the = sign. Is it however also possible to align on more than one place in the environment? I would also like the \text to be aligned, as wel as the begining of each new line.
116802
I have the following assignment:  Let $A_i= \left \{...,-2,-1,0,1,...,i \right\}$.   Find  a) $\displaystyle \bigcup_{i=1}^{n} A_i$   b) $\displaystyle \bigcap_{i=1}^{n} A_i$  I think the  first one is:  $\displaystyle \bigcup_{i=1}^{n} \left \{...,-2,-1,0,1,...,i \right\} = \left \{...,-2,-1,0,1,2...,n \right\}$  But what about the second one?
51704
Why does the \pm sign is ower compared to the number next to it? Is it normal behaviour? How can I raise it so to be at the same level as the number?  My distribution is Vanilla TeX and it is installed less than a week ago so it is updated.    \documentclass{article}  \usepackage[top=0.7in, bottom=1.2in, left=0.8in, right=0.8in]{geometry}  \usepackage{parskip}  \setlength{\parindent}{0cm}  \usepackage{amsmath}  \usepackage{unicode-math}  \usepackage{fontspec}  \usepackage[greek,english]{babel}  \setmainfont [     Ligatures=TeX,     Extension=.otf,     UprightFont=*,     BoldFont=*Bold,     ItalicFont=*It,     BoldItalicFont=*BoldIt,     Mapping=tex-text ]{GFSArtemisia}  \setsansfont[Mapping=tex-text]{GFSArtemisia.otf}  \setmathfont{latinmodern-math.otf}  \setmathfont[range=\varnothing]{Asana-Math.otf}  \setmathfont[range=\int]{latinmodern-math.otf}  \begin{document}  $$x= \pm 1$$  \end{document}