## 2.1. Countable Infinity

### Examples 2.1.7(c):

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.