From a pdf textbook:
Example (infinite sets having the same cardinality). Let f : (0, 1) → (1,∞) be
defined by f(x) = 1/x. Then f is a 1-1 correspondence. (Exercise: prove it.) Therefore,
|(0, 1)| = |(1,∞)|.
Exercise. Show that |(0,∞)| = |(1,∞)| = |(0, 1)|. Use this result and the fact that
(0,∞)...