Can anyone help me with this Advanced Multivariable Calculus

Can anyone help me with this Advanced Multivariable Calculus question?

Problem 6. Suppose c is a positive number and R denotes the set of all rational numbers in the number interval I [0,1]. Is there an open set O that contains the set R, such that the length of O is less than c? Explain your answer using English sentences.

Solution

Since c is not mentioned, Let c=1.2

Then we can take the open interval (-0.01, 1.1), the length of which is 1.11<c

Also [0,1] is contained in (-0.01, 1.1).