First Assignment

The most challenging question of the first assignment would have to be question 4. I didn’t know how to approach the question to begin with. But after wrestling with it for awhile and getting help on it, the question started to make sense to me. Proving the contradiction was a bit tricky, because we had to choose the well ordering principle. I had to prove that there exists a smallest numerator for a quotient representing the golden ratio. This led to the required contradiction proving that the golden ratio is an irrational number, which I used to answer the last part of the question: proving 5^1/2 is irrational.