Examples 2.1.7(c):

The set of all polynomials with integer coefficients is countable.
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Let P be the set of all polynomials with integer coefficients, and define the set P(n) to be the set of all polynomials with integer coefficients and degree n. From before we already know that P(n) is countable. But
Hence, P is the countable union of countable sets, and must therefore be countable itself by our result on countable unions of countable sets.

Interactive Real Analysis, ver. 1.9.5
(c) 1994-2007, Bert G. Wachsmuth
Page last modified: Mar 28, 2007