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Let be a function defined on.
Let be a function defined by (2.2).
Let f be a function defined in Definition 3.
and let be a function defined on a neighborhood of.
Let be a function defined on, valued in.
Let f be a function defined on (mathbb{N}_{0}).
Let f be a function defined on (mathbb{N}_{a}).
Let f be a function defined on ([0,1]).
Let f be a function defined on ([0,a]).
Let f be a function defined on ([a, b]).
Let f be a function defined on (J_{k}).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com