Notes for Math 345
نویسنده
چکیده
Proof. First, we’ll give an intuitive proof. Let b > 0 be given. Mark off multiples of b on the number line. The integer a will fall between two different multiples. qb is the smaller multiple, and r is the distance from qb to a. Clearly the choices of q and r are unique. Why we need the well-ordering principle: it’s not clear that a will fall between two different multiples of b if the numbers a and b are very large.
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