Interactive Real Analysis
- part of 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
BackHence, P is the countable union of countable sets, and must therefore be countable itself by our result on countable unions of countable sets.