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and note that.
Put, and note that.
Let,,, and note that ; then (2.5).
Then for any and, note that (3.18).
Suppose that and note that ; then inequality (2.11) is equivalent to (2.13).
Therefore, all the assumptions of Theorem 3.2 are satisfied, and note that.
We have ; then (4.3). is independent to, and, and note that ; then (4.4).
We define relative rounding errors and note that.
Do measure the basement and note that figure separately on the listing form.
And note that "somewhat slower pace".
And note that careful, exact, poignant "room 5".
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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