I need help for the question below, i simply do not know where to start.
In the proof of the quotient remainder theorem, we have "if n>=0 and 0<d<=n, then there is a largest integer q such that qd<=n". Use the well ordering principle to justify the existence of q. (Consider the set S={i element of Natural numbers: id<=n}).
Given with we want to show there exists so that where . Define the set . This set is non-empty (why?) and so by Well-Order it means there is a that is the least element. Thus, for some . We will show , because if not then where . And then which is impossible since is the least element and .