In this exercise we outline a proof that  by Exercise 13, it suffices to show that (a) To...

In this exercise we outline a proof that  by Exercise 13, it suffices to show that

(a) To show that  we define a function  

Show that f is injective.

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(b) To show that  we use Exercise 19(b) to conclude that Thus it suffices to find an injection  Use the fact (Theorem 3.3.12) that given such that a < r < b to show that f is injective.