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How do you show that R is uncountable?

Updated: 4/28/2022
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10y ago

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One way is Cantor's diagonal argument. See link.

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Q: How do you show that R is uncountable?
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Proof By Contradiction:Claim: R\Q = Set of irrationals is countable.Then R = Q union (R\Q)Since Q is countable, and R\Q is countable (by claim), R is countable because the union of countable sets is countable.But this is a contradiction since R is uncountable (Cantor's Diagonal Argument).Thus, R\Q is uncountable.


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