# Proof of Transcendentals Uncountable

1. Sep 8, 2010

### mynameisfunk

Hi guys,
My question is to prove that the set of algebraic numbers is countable, then also prove that the set of transcendentals are uncountable. I have already proved the countability of the algebraics but now i do not know how to proceed. I beleive it could be as simple as the complement of the algebraics in R is uncountable, but I am not sure if the complement of the algebraics numbers within R is the set of transcendentals or not. I was unable to find out if this is the case.. I saw that trascendtals could possibly be complex, but in any case, if transcendentals make up the rest of R, then I would be done.. Any help would be great.. If anyone needs to see my proof of algebraics being countable I will post if someone asks.
Thanks

2. Sep 8, 2010

### CompuChip

Isn't a trascendental number by definition any number which is not algebraic?
And that R - A is uncountable for any countable (or finite, of course) subset A is a general theorem.
So I think you are done.