Define injections g : [0, 1) → [0, 1] and h : [0,1] → [0, 1). Prove that that the functions g and h that you define are injections. It follows from the Cantor-Schroeder-Bernstein theorem that there...

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Extracted text: Define injections g : [0, 1) → [0, 1] and h : [0,1] → [0, 1). Prove that that the functions g and h that you define are injections. It follows from the Cantor-Schroeder-Bernstein theorem that there exists a bijection f : [0, 1] → [0, 1). (Can you see how to define such a bijection directly?)