Are their any restraints on how you define subset?
Maybe it has to be a classical set (i.e., natural numbers, integers, etc...)?
Otherwise (let S be the subset), the smallest subset of the real number set that contains [tex] \sqrt{64}=8 [/tex] would be S={8}.
As this subset only contains the required element (i.e., [tex]|S|=1[/tex]), hence is the smallest possible subset.
