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The phrase "arithmetic and the" is not correct and does not form a complete thought in written English.
It may be used in contexts where it is part of a larger phrase or sentence discussing arithmetic, but it needs additional information to be meaningful.
Example: "In the study of mathematics, arithmetic and the principles of algebra are foundational."
Alternatives: "arithmetic and its" or "arithmetic and the concepts of".
Exact(57)
The electoral arithmetic and the early opinion polls both favour Mr Sarkozy.
Nice try: but this line of argument ignores both arithmetic and the testimony of voters.
But the electoral arithmetic and the electoral logic are stronger than most commentators seem to have acknowledged.
We make the mistake of applying arithmetic and the mechanics of the economic world to the living state.
The root of the dismal arithmetic, and the chancellor's most fundamental problem, is the suddenly feebler economy.
Maya attempts to subvert Sohail's strictness and dogma by teaching Zaid arithmetic and the alphabet and eventually staging a rescue.
May's embrace for a softer Brexit has therefore changed the Commons arithmetic – and the political calculations that come with it.
There were a few Qurʾānic schools among the Fur, in which elementary Arabic, arithmetic, and the Qurʾān were taught.
Similar(3)
The filter can be implemented using three circular buffers to simplify the arithmetic and reduce the computation time.
Dedekind's and Frege's original contributions consisted in particular, detailed reductions of, on the one hand, analysis to arithmetic and, on the other hand, arithmetic to logic.
Heyting arithmetic, after all, has exactly the same axioms as Peano arithmetic, and is the logical closure of those axioms under intuitionistic, rather than classical, logic.
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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