This article is written in my own words. All the information contained within this article was taken from the internet and is not my original material. I am only sharing what has been published on other websites and sources online, without adding anything new.
This article is written in my own words. All the information contained within this article was taken from the internet and is not my original material. I am only sharing what has been published on other websites and sources online, without adding anything new.
The amsbook class (LaTeX) includes the end of proof symbol, known as QED. The default version uses an empty square for this purpose, but you can redefine the symbol to be a filled square or even the word “QED” itself.
If you’re going to use amsthm’s proof environment, it adds an end-of-proof symbol automatically at the conclusion of the environment. It also places extra spacing before that symbol. You may wish to keep the default appearance of the ending mark, or change it to something else.
A minimal complete document that adds the ending mark automatically to a proof ending in ordinary text looks like this:
\documentclass{article}
\usepackage{amsthm}
\begin{document}
\begin{proof}
Placeholder proof text.
\end{proof}
\end{document}
As you can see, there are two things: the label for the proof (the italicized “Proof”) and the space before the end of the proof marker. By default, LaTeX places an empty square after the conclusion of a proof.
But if you want to change how that marker appears, you’ll need to adjust the definition of \qedsymbol, which controls its appearance. The package amssymb provides a number of symbols, including the filled square, $\blacksquare$, which we will use later.
Default
The following example keeps the default appearance of the ending mark. We don’t have to do anything special; we just use the package as provided.
\documentclass{article}
\usepackage{amsthm}
\begin{document}
\begin{proof}
The sum of 1 + 2 = 3.
\end{proof}
\end{document}
The package amsthm defines the command \qedsymbol which defaults to the hollow square. You can override this by changing the definition of \qedsymbol. However, we won’t do anything here. We’ll just leave it alone.
Filled Square
To make the ending mark appear as a filled square, we need to load both amsthm and amssymb. In addition, we’ll have to define the \qedsymbol to display the square symbol instead of the default hollow one.
\documentclass{article}
\usepackage{amsthm}
\usepackage{amssymb}
\renewcommand\qedsymbol{$\blacksquare$}
\begin{document}
\begin{proof}
The sum of 1 + 2 = 3.
\end{proof}
\end{document}
The ending mark looks like this: ■. Note that because it’s defined inside math delimiters, it displays correctly. Otherwise, it would not.
QED
In this example, we’ve replaced the default ending mark with the word “QED.” Instead of using the square symbol, we used the regular text. That means we didn’t need to import the amssymb package. We simply changed the definition of \qedsymbol to the word QED.
\documentclass{article}
\usepackage{amsthm}
\renewcommand\qedsymbol{QED}
\begin{document}
\begin{proof}
The sum of 1 + 2 = 3.
\end{proof}
\end{document}
The ending mark looks like this: QED.