Let f : (0, 1] R be given by f(r) = r and g :...

 

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Let f : (0, 1] → R be given by f(r) = r and g : R→ [0, 1] be given by g(x) = 1 Prove that |[0, 1]= R| using the Cantor-Schröder-Bernstein Theorem and provide an explicit description of the bijection constructed by the proof of the theorem. Let f : (0, 1] → R be given by f(r) = r and g : R→ [0, 1] be given by g(x) = 1 Prove that |[0, 1]= R| using the Cantor-Schröder-Bernstein Theorem and provide an explicit description of the bijection constructed by the proof of the theorem.