splitting long text-containing equation: it becomes right-aligned?

Question

So, first off, I am completely new to LaTex and actually opened my first document today. I use texlive, and the amsmath package is also used here.

I want to write down my proof that the continuum hypothesis is equivalent to a certain proposition. My proof consists of two implications, that I would like to specify before I start proving them. So now I'm trying to make a nice implication that I can refer to later (I was thinking equation-environment), that is centered. Since the implication is between two propositions, it just contains text and a \Longrightarrow. It is too long to fit in the page, so I wanted to break it, placing the first statement on top, the arrow in the middle and the second statement at the bottom. I having bene looking on the internet for hours, and {split} worked, except that now everything is aligned at the right of the page, which isn't my intention. It should be centered. Can anybody help me out? {multline},{align*},{align},{eqnarray},...all weren't recognised by LaTeX.

This is my code for the "equation":

\begin{equation}
\begin{split}
\label{implication}
 {\displaystyle \textit{De continu\"umhypothese}}\\ 
 \Longrightarrow \\
 {\textit{Als $X$ een overaftelbare deelverzameling is van $\mathbb{R}$,}} 
{\textit{ dan is er een bijectie van $X$ naar $\mathbb{R}$.}}
 \end{split}
\end{equation}

And it comes out like this:

Thank you very much!

Answer 1

i've taken some liberties here, but i think this is close to what you want.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amsfonts}

\begin{document}    
show cross-reference: \eqref{implication}
\begin{multline}
\label{implication}
 \text{\textit{De continu\"umhypothese}}\\ 
\Longrightarrow \quad
\begin{aligned}[t]
 & \text{\textit{Als $X$ een overaftelbare deelverzameling is van $\mathbb{R}$,}} \\
 & \text{\textit{ dan is er een bijectie van $X$ naar $\mathbb{R}$.}}
 \end{aligned}
\end{multline}
\end{document}

• added the packages amsmath and amsfonts
• changed equation to multiline. this multiline environment will set the first line to the left, and the last line to the right.
• used the aligned sub-environment to mutually align the last two lines; the & is needed to left-align, and the [t] top-aligns the sub-environment with what's on the left-hand side. \split does not work in this situation.
• placed the \Longrightarrow on the same line as the right-hand side expression.
• made the strings of words \text; without it, evenn \textit is treated as math, and spaces are ignored.
• applied the \label to the outermost environment; if used inside split (or aligned) it may get lost when used with \eqref.

Answer 2

You might have this equation displayed over three lines, based on flalign:

\documentclass[a4paper, dutch]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage[showframe]{geometry}
\usepackage{mathtools, amsfonts}

\begin{document}

\begin{flalign}
\label{implication}
 & \begin{gathered}[b]
  \textit{De continuümhypothese}\\
  \Longrightarrow
  \end{gathered} & & \\
 & \rlap{\textit{Als $X$ een overaftelbare deelverzameling is van $\mathbb{R}$, dan is er een bijectie van $X$ naar $\mathbb{R}$.}}\notag
 \end{flalign}

\end{document}