[Tex/LaTex] What do the pieces of LaTeX, \left and \right, respectively mean

delimitersmath-mode

What are their uses and are they even standard?

Best Answer

\left and \right are used for delimiters when they have to change the size dynamically depending on the content. Consider the following example:

\documentclass{article}
\usepackage{amsmath}


\begin{document}
Compare this:
 \begin{align*}
 \left(\sqrt{2}+\sqrt{3}\right)^2
            &=\left(\sqrt{2}\right)^2+2\times\sqrt{2}\times\sqrt{
                3}+\left(\sqrt{3}\right)^2\\
            &=2+2\sqrt{6}+3\\
            &=5+2\sqrt{6}
\end{align*}
with:
\begin{align*}
 (\sqrt{2}+\sqrt{3})^2
            &=(\sqrt{2})^2+2\times\sqrt{2}\times\sqrt{
                3}+(\sqrt{3})^2\\
            &=2+2\sqrt{6}+3\\
            &=5+2\sqrt{6}
\end{align*}
First one uses \verb|\left(| and \verb|\right)| and second one uses just \verb|(| and \verb|)|. I hope the difference is clear. 

Just another example:    
\[\left(\frac{1}{2}\right) \qquad (\frac{1}{2})\]

\end{document}

enter image description here

In this particular case, the (\sqrt{2}+\sqrt{3}) with \left and \right gives bit bigger parenthesis making it to look ugly (to some extent) as noted by Enrico. In such cases, proper variant of delimiters (\bigl and \bigr in this case) may be used to get the appropriate height.

For more details, refer to amsmath documentation - page 15, section 4.14 (texdoc amsldoc from command prompt). Here is a screen shot of the same:

enter image description here

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