Here's a good one, from Kenneth Rosen's book on Discrete Mathematics. We just covered countability a few blogs back, so you should be able to answer this one.
A number, call it x, is said to be algebraic if there exists a polynomial, call it p, with integer coefficients (for example, 5x^8 + 2x^4 + 90) such that p(x) = 0. Prove that the collection of algrbraic numbers is countable.
posted by FlyingSheep @ 4:50 PM
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