How do I show that a set of algebraic numbers is countable?

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- Feb 10th 2011, 02:22 PMrickyalgebraic numbers
How do I show that a set of algebraic numbers is countable?

- Feb 10th 2011, 02:41 PMDrSteve
The algebraic numbers are the roots of polynomials with integer coefficients. A polynomial of degree n has at most n roots. There are countably many integers. The polynomials can easily be put into one to one correspondence with the set of finite sequences of integers which is countable. Now see if you can put all this together.