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Of course solving arithmetical problems in arithmetic is in some cases practically impossible.
Then Kurt Gödel proved that there exist arithmetical statements that are undecidable in Peano Arithmetic (Gödel 1931).
More precisely, they attempted to construct a derivation of arithmetical principles from definitions of arithmetical concepts, using only logical laws.
He calls that arithmetical.
"It's an arithmetical fact".
Once again numbers, arithmetical language.
I. Arithmetical Determinations of Number.
Some indices incorporate arithmetical problems.
Subsistence increases only in an arithmetical ratio.
The distributive justice follows an arithmetical model.
An arithmetical illustration may be helpful here.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com