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What LaTeX commands should I use to center the equations on the page, but without numbering them?

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You can use the environment align* of the package amsmath. It centers the equations, and the * in the name prevents it to number the formulas.

Example :

\begin{align*}
f^* : ]0,+\infty[ &\rightarrow \mathbb{R}\\
m &\mapsto (m+1)e^m-me^m = e^m
\end{align*}
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