arithmetic

Arithmetic operates on numbers — addition, subtraction, multiplication, division are all operations defined over numbers. Remove the concept of number and arithmetic stops operating: there is nothing to operate on.

Arithmetic is a branch of mathematics — its accepted definition carves it as the branch concerned with operations on numbers and the study of the properties of certain algebraic structures arising from +, -, x, /. Direction is specific-to-general: a branch is a specific KIND of its parent field (a kind of doing mathematics), not a mere topic studied within it, so Law 9a does not bar it; and it is not a component part, so not CONTAINS. Nearest kind (Law 11e): mathematics (cmrg4vstb00kx2a1nar61eoe7) is the closest existing kind — no intermediate field stands nearer — and the board has already accepted the identical branch-to-field relation for numerical-analysis and linear-algebra, both INSTANCE_OF mathematics. This also corrects the just-struck arithmetic-to-computation leap, whose target is a process, not the field the branch belongs to.

Calculator is designed and maintained for the sake of arithmetic — it performs arithmetic operations (addition, subtraction, multiplication, division) on behalf of users. Remove arithmetic and the calculator has no purpose. The teleological arrow points correctly: servant (calculator)→master (arithmetic).