Find the infimum and supremum of the set of real numbers in $(0, 1)$ whose decimal expansion contains only$ 0’s$ and $ 1’s$
Infimum of this set is $0$, Supremum should be $0.111111...$ Supremum of this set is not clear to me. Is there any specific number equivalent to $0.1111...$ which can be considered as supremum of this set. If no, then what is the supremum$?$