# Prove that there is not smallest positive real number.Prove that square root of 5 is irrational

Feb 3rd, 2012
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Theorems :- Prove that there is not smallest positive real number. & Prove that square root of 5 is irrational.

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Theorem : Prove that there is not smallest positive real number.Proof : Assume that x is the smallest positive real number. Consider x/2. We know x/2 is real. Also, x/2 < x. This is a contradiction, thus such x does not exist and there is no smallest positive real number. In your proof, "x is a pr

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