test-lua.tex

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The foundations of the rigorous study of {\it analysis} were laid in the nineteenth century, notably by the mathematicians Cauchy and Weierstrass. Central to the study of this subject are the formal definitions of {\it limits} and {\it continuity}.
Let $D$ be a subset of $\bf R$ and let $f \colon D \to {\bf R}$ be a real-valued function on $D$. The function $f$ is said to be {\it continuous} on $D$ if, for all $\epsilon > 0$ and for all $x \in D$, there exists some $\delta > 0$ (which may depend on $x$) such that if $y \in D$ satisfies $$|y - x| < \delta$$ then $$|f(y) - f(x)| < \epsilon.$$
One may readily verify that if $f$ and $g$ are continuous functions on $D$ then the functions $f+g$, $f-g$ and $f\cdot g$ are continuous. If in addition $g$ is everywhere non-zero then $f/g$ is continuous.

Et voici quelques caractères accentués.

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