I agree that the set of all math books is countable, and I agree that there are uncountably many f_epsilon functions if epsilon comes from an uncountable set.

I agree that the set of all math books is countable, and I agree that there are uncountably many f_epsilon functions if epsilon comes from an uncountable set. However, f(x) = x + epsilon is not a computable function when epsilon is not a computable number. So not all of the f_epsilon family of functions is computable.