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I have given from class that the Lebesgue measure of [0,1] intersects Q(irrational numbers) equals to 0. I don't understand why this is true. Since

I have given from class that the Lebesgue measure of [0,1] intersects Q(irrational numbers) equals to 0. I don't understand why this is true. Since I think that there are infinity irrational numbers are in interval [0,1]. Can you explain this for me

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