5:26 PM
Can we prove that $\mathbb{R}\times\mathbb{R}$ is uncountable by a proof of contradiction and using an explicit function?
For example, suppose $\mathbb{R}\times\mathbb{R}$ is countable, that means there exists a function $f:\mathbb{R}\times\mathbb{R}\to\mathbb{N}$ which is injective.
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