Why must the remainder $r$ be the smallest nonnegative integer of the form $a-bn$ when applying the division algorithm to $a$ and $b$? In the proof of the division algorithm, we use the fact that the set of all nonnegative integers of the form $a-nb$ is nonempty and the well ordering principle to show that $r$ exists, but must $r$ be the least element of that set?
2026-04-13 10:21:12.1776075672
Remainder and well ordering principle
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