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# Is Sweater countable?

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### How prove that the set of irrational numbers are uncountable?

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.