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
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Duplicates: 1, 2, 3, 4. – Kenny Lau Sep 10 '17 at 17:20
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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
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if we integrate this function from 0 to 1 that gives us a number. – Seyed Moein Ayyoubzadeh Sep 10 '17 at 17:20
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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
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@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
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What you need is Lebesgue Integration. – Brevan Ellefsen Sep 10 '17 at 18:28