Intuition of upper & lower bound of sequence of subsets. I have come across these while studying the limsup & liminf of sequence of subset of a set. In order to understand that, I have to understand what least upper bound & greatest lower bound of a sequence of subset mean. I would be grateful if anyone helps me comprehend this concept intuitively as I am new & novice to this topic.

$x$ is in the lim sup of a sequence of sets if and only if it is in infinitely many of the sets.  
And $x$ is in the lim inf of a sequence of sets if and only if it is in all but finitely many of the sets (or equivalently if it is in all the sets from some point on).
