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Show that cardinality of R^2 is cardinal number of continumm

Quote: Originally Posted by math.dj Show that cardinality of R^2 is cardinal number of continumm $\displaystyle |\mathbb{R}\times \mathbb{R}| = |\mathbb{R}|\cdot |\mathbb{R}| = 2^{\aleph_0} \cdot 2^{\aleph_0} = 2^{\aleph_0 + \aleph_0} = 2^{\aleph_0}=|\mathbb{R}|$