i want to prove: from 0 to 1 number of Rational numbers are fewer than Irrational numbers. How does i prove that? (Thanks and sorry for my awful English :D)
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Look up Cantor diagonal argument – b00n heT Sep 10 '17 at 17:16

Duplicates: [1](https://math.stackexchange.com/q/787650/328173), [2](https://math.stackexchange.com/q/732/328173), [3](https://math.stackexchange.com/q/474415/328173), [4](https://math.stackexchange.com/q/10333/328173). – Kenny Lau Sep 10 '17 at 17:20

i want to solve it with integration.i saw a function that his value in rational numbers is 1 and in irrational is 0 . – Seyed Moein Ayyoubzadeh Sep 10 '17 at 17:20

if we integrate this function from 0 to 1 that gives us a number. – Seyed Moein Ayyoubzadeh Sep 10 '17 at 17:20

if our number near 0 we find out the number of irrational number is more than rational. – Seyed Moein Ayyoubzadeh Sep 10 '17 at 17:22

@SeyedMoeinAyyoubzadeh I suggest that you should edit your question to indicate that you hope to prove this using the integration of the function mentioned. (Not everyone approves of clarifying a question in the comments. It is better to edit the question.) – Jim H Sep 10 '17 at 17:44

What you need is Lebesgue Integration. – Brevan Ellefsen Sep 10 '17 at 18:28