0
votes
2answers
218 views

Algebraic and Transcendental Numbers - Set Theory

Denote $\mathbb Q$$[x]$ = set of polynomials with coefficients $c_1$, $c_2$, $...$ ,$c_n$ in $\mathbb Q$. A number $a$ is algebraic if there exists a polynomial $f(x)$ in $\mathbb Q$[x] such that ...
6
votes
3answers
644 views

How do we prove the existence of uncountably many transcendental numbers?

I know how to prove the countability of sets using equivalence relations to other sets, but I'm not sure how to go about proving the uncountability of the transcendental numbers (i.e., numbers that ...