Graduate Proofs
Proofs written during graduate study in mathematics.
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Proof Irrational Square Roots
The square root of n is rational only for perfect squares: a descent proof with no primes, and one by Euclid's lemma.
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Proof The Golden Ratio is Irrational
Three proofs that phi is irrational: descent from phi = 1 + 1/phi, the rational root test, and its endless continued fraction.