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Apparently it's aleph null, but I really don't understand why or how to form a bijection between the two sets, Z[x] and Z.

Zympan
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  • Does this answer your question? Show that the set of polynomials with rational coefficients is countable. – Anne Bauval Sep 27 '22 at 11:40
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    A common error here is to forget that polynomials strictly have finitely many nonzero coefficients. Do not confuse polynomials with formal power series which may have infinitely many nonzero coefficients. These are similar but not the same objects. Use what makes them different to your advantage. – JMoravitz Sep 27 '22 at 11:46
  • In many cases , we do not establish the bijection to prove the countability , but argue with known properties of countable sets (for example when unions are again countable). The key is in fact that polynomials have FINITE many coefficients. This even makes the set of algebraic numbers countable ! – Peter Sep 27 '22 at 13:51

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