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

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 same cardinality.

(b) Show that the intervals (0, 1) and (0, ∞) have the same cardinality. (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 have the same cardinality. (Hint: tan^-1x.)

Expert Solution

Colby Messinger answered 2 years ago

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

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