how to prove there is no Lebesgue number for open cover (1/n,1)?

[ramasamyg]

I am not sure how to prove there is no Lebesgue number for an open cover {(1/n,1)} of interval (0,1). If I take any element x of (0,1), it is inside any of the open set Ux = (1/n,1) of the open cover. So I am not sure how taking a ball of radius r around x is not contained in any Ux.

[lurflurf]

This should be easy. Do it the other way round.
Think about the subintervals of (0,1) that are not contained within (1/n,1).