How do Sudoku puzzles use numbers without requiring arithmetic?

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Sudoku puzzles do not require arithmetic because they are based entirely on logic rather than mathematical calculation.1

In a standard 9×9 grid, the objective is to place the numbers 1–9 exactly once in each row, column, and designated 3×3 subgrid. Because the numbers serve only as distinct symbols or placeholders to satisfy these positional constraints, their numerical value is irrelevant to the solution process. The challenge relies on deductive reasoning to determine which symbol belongs in a specific square based on the existing entries, rather than performing any addition, subtraction, or other arithmetic operations.1