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Let (x=x_{0}in A) be an arbitrary point.
Initialization: Given a tolerance, fix an arbitrary point and choose,.
In this system, an arbitrary point O (the origin) is chosen on a given line.
Free range is ultimately an arbitrary point between the wild and the domesticated.
Take an arbitrary point (x^{ast}inGamma).
Let be an arbitrary point in for.
Let be an arbitrary point in.
We fix an arbitrary point x ∈ Ϝ.
Initialization: Fix an arbitrary point and set.
Now let be an arbitrary point of.
Let x0∈X be an arbitrary point.
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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