Exercise 2.4.3 (Challenging): Suppose F is an ordered field that contains the rational numbers, such that Qis dense, that is: Whenever x, y = F are such that x < y, then there exists a q EQ such that x 0, there exists an M such limit - that for all n,k> M, we have |xn − xk| <ɛ. Suppose every Cauchy sequence of rational numbers has a in F. Prove that F has the least-upper-bound property.

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