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Exercise We say that |A| = |B| if there exists a bijection f : A ?...

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Advance Math

Exercise We say that |A| = |B| if there exists a bijection f : A? B.

(a) Show that the intervals [1, 2] and [3, 7] have the samecardinality.

(b) Show that the intervals (0, 1) and (0, ?) have the samecardinality. (Hint: First try (0, 1) and (1, ?) (later subtract 1).Identify numbers small numbers in (0, 1) with large numbers in (1,?) somehow.)

(c) Show that the interval (0, 1) and the real numbers R havethe same cardinality. (Hint: tan-1x.)

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