Friday, 31 January 2014

elementary set theory - Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) times (0, 1)$ have the same cardinality

Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
using the SB theorem?
Also how does one find a bijection on $f:(0, \infty) \to (0,1)$ such that they have the same cardiniality?

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