# Decrease the distance between these two formulas

How can I decrease the distance between the following two formulas?

\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{vietnam}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage[margin=2cm]{geometry}
\usepackage{enumerate}
\usepackage{mathrsfs}
\usepackage{afterpage}
\begin{document}
\noindent\\
Ta có: $$\begin{array}{c} \forall y \in \alpha + [(-\alpha+E) \cap A] \Leftrightarrow y- \alpha \in (-\alpha +E) \cap A \Leftrightarrow \text{ \begin{cases} y-\alpha \in -\alpha +E \\ y- \alpha \in A \end{cases}}\Leftrightarrow \text{ \begin{cases} y \in E \\ y \in \alpha+A \end{cases}} \end{array}$$
$$\begin{array}{c} \forall y \in \alpha + [(-\alpha+E) \setminus A] \Leftrightarrow y- \alpha \in (-\alpha +E) \setminus A \Leftrightarrow \text{ \begin{cases} y-\alpha \in -\alpha +E \\ y- \alpha \notin A \end{cases}}\Leftrightarrow \text{ \begin{cases} y \in E \\ y \notin \alpha+A \end{cases}} \end{array}$$
Ta chứng minh $x+A$, $xA$ là $L$-đo được.
\end{document}


First of all: sorry, my editor cannot deal with your accented characters, so I had to drop them. Then

1. You should not put a cases environment in \text{$...$}, but you do not need cases here anyway. The case environment expects two columns, which is why it introduces the extra space here.
2. Please do not use $$...$$, but $...$ instead.
3. You can use an array here.
4. I had a little help from David Carlisle.

\documentclass[12pt,a4paper]{article}
\usepackage[margin=2cm]{geometry}
\usepackage{amsmath}
\begin{document}

Ta co: \begin{gather*}
\forall y \in \alpha + [(-\alpha+E) \cap A]
\Leftrightarrow y- \alpha \in (-\alpha +E) \cap A \Leftrightarrow
\left\{\begin{array}{@{}l@{}}
y-\alpha \in -\alpha +E \\
y- \alpha \in A
\end{array}\right. \Leftrightarrow
\left\{\begin{array}{@{}l@{}}
y \in E \\
y \in \alpha+A
\end{array}\right.
\\
\forall y \in \alpha + [(-\alpha+E) \setminus A] \Leftrightarrow y- \alpha \in (-\alpha +E) \setminus A \Leftrightarrow
\left\{\begin{array}{@{}l@{}}
y-\alpha \in -\alpha +E \\
y- \alpha \notin A
\end{array}\right.\Leftrightarrow
\left\{\begin{array}{@{}l@{}}
y \in E \\
y \notin \alpha+A
\end{array}\right.
\end{gather*}
Ta chung minh $x+A$, $xA$ la $L$-do duoc.
\end{document}


One may also use aligned.

\documentclass[12pt,a4paper]{article}
\usepackage[margin=2cm]{geometry}
\usepackage{amsmath}
\begin{document}

Ta co:
\begin{aligned} \forall y \in \alpha + [(-\alpha+E) \cap A] \Leftrightarrow y- \alpha \in (-\alpha +E) \cap A \Leftrightarrow &\left\{\begin{aligned} &y-\alpha \in -\alpha +E \\ &y- \alpha \in A \end{aligned}\right. \Leftrightarrow \left\{\begin{aligned} &y \in E \\ &y \in \alpha+A \end{aligned}\right. \\ \forall y \in \alpha + [(-\alpha+E) \setminus A] \Leftrightarrow y- \alpha \in (-\alpha +E) \setminus A \Leftrightarrow &\left\{\begin{aligned} &y-\alpha \in -\alpha +E \\ &y- \alpha \notin A \end{aligned}\right.\Leftrightarrow \left\{\begin{aligned} &y \in E \\ &y \notin \alpha+A \end{aligned}\right. \end{aligned}
Ta chung minh $x+A$, $xA$ la $L$-do duoc.
\end{document}


• too adjacent display math :( (gather is designed for that) May 24 '20 at 8:59
• @DavidCarlisle Thanks! Better now? (I just can't remember gather, for some reason it always becomes \begin{gopher} and then LaTeX gives me an error.)
– user194703
May 24 '20 at 9:06
• if I was being picky I'd say that the "One may also use" could say "The above is wrong but you could instead use" but I'm not picky so +1 :-) May 24 '20 at 9:09
• @DavidCarlisle OK, my editor had the old version in the buffer. Sorry and thanks!
– user194703
May 24 '20 at 9:10
• because tex just doesn't do anything sensible if display math is at start of a paragraph or immediately following another display math (I think I have an answer giving gory details somewhere, I'll see if I can find) May 24 '20 at 9:12

Hope it works as desired! Just use the setspace package and control the setstretch option. And try to use $...$ instead of $$...$$.

\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{vietnam}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage[margin=2cm]{geometry}
\usepackage{enumerate}
\usepackage{mathrsfs}
\usepackage{afterpage}
\usepackage[nodisplayskipstretch]{setspace}
\setstretch{.75}

\begin{document}
\noindent\\
Ta có: $$\begin{array}{c} \forall y \in \alpha + [(-\alpha+E) \cap A] \Leftrightarrow y- \alpha \in (-\alpha+E) \cap A \Leftrightarrow \text{ \begin{cases} y-\alpha \in -\alpha +E \\ y- \alpha \in A \end{cases}}\Leftrightarrow \text{ \begin{cases} y \in E \\ y \in \alpha+A \end{cases}} \end{array}$$
$$\begin{array}{c} \forall y \in \alpha + [(-\alpha+E) \setminus A] \Leftrightarrow y- \alpha \in (-\alpha +E) \setminus A \Leftrightarrow \text{ \begin{cases} y-\alpha \in -\alpha +E \\ y- \alpha \notin A \end{cases}}\Leftrightarrow \text{ \begin{cases} y \in E \\ y \notin \alpha+A \end{cases}} \end{array}$$
Ta chứng minh $x+A$, $xA$ là $L$-đo được.
\end{document}

• never have \noindent\\  and never have adjacent display math, a multi-line display such as gather should be used. May 24 '20 at 8:59