1. The problem statement, all variables and given/known data Prove that the interval [0,1] is not a zero set. 2. The attempt at a solution Assume for contradiction that the interval [0,1] = Z is a zero set. This mean that given epsilon greater than 0, there is a countable coverage of Z by open intervals (ai, bi) (___I don't know what those intervals should be...___) such that the summation of bi - ai is less than epsilon. But since Z is uncountable, there cannot be a countable coverable of Z by open intervals. Thus Z is not a zero set.