I am not a mathematics student, but just out of curiosity I was checking out a website which explains the basics of 'Chaos Theory' to the layman. In this site was the sentence : transcendental ...
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 ...
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 ...