Let C0 be the set of all continuous functions from [a,b] to R

Let A = { f http://upload.wikimedia.org/math/7/b...e1a4c7cff0.png C0: f(q) is irrational for all q http://upload.wikimedia.org/math/7/b...e1a4c7cff0.png Q} where Q is the set of rational numbers.

The question is: Is A a thick subset of C0.

EDIT: The answer I had here was very wrong