Irrational FractionPro Problems > Math > Logic > Proofs > Indirect Proofs
Let a and b be positive integers, with b not a perfect square. Show that the following expression is irrational, using an indirect proof.
Hint: Remember that an irrational number is a number which cannot be written as the quotient of two integers.
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For every positive rational number x, there exists a smaller positive rational number y. Prove this statement by indirect proof.
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Use an indirect proof to show that there are infinitely many prime numbers.
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Hint: This is a more generalized version of the problem found here: X Squared Proof
Create an indirect proof for the following statement: The harmonic mean of any two positive numbers lies inclusively between the two numbers.
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