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"for the completeness" is a valid phrase in formal written English.
It can be used to describe an action taken in order to make something as complete as possible. For example, "The lecturer worked extra hours to finish the lecture, for the completeness of his presentation."
Exact(60)
It makes clear that reports posted on the site are added by users and therefore it is not responsible for the completeness or correctness of the information.
"More and more I felt greater responsibility for the completeness, accuracy and perfection in all the parts," he wrote to his editor to explain the delays.
For the completeness, we include the proof here.
For the completeness, we state the proof as follows.
NC-approximation schemes for various NP-Hard and PSPACE-Hard problems restricted to geometric graphs are developed in [31].
For the completeness of the paper, we give proofs below.
Therefore, AUV can be launched without waiting for the completeness of the alignment.
The nonlinear finite element implementation details are also presented for the completeness of the method.
Because of this and for the completeness, we will sketch their proofs.
However, for the completeness of the proof, we give the following proof with some modifications.
For the completeness of the structure of the paper, we write down the proofs.
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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