Bounded
Elementary
A set of numbers is bounded if it does not go on forever in either direction: there is some number that all of them are smaller than in size.
High school (sets of real numbers)
A set $S$ of real numbers is bounded if there is a number $M$ with $\lvert x \rvert \leq M$ for every $x \in S$.
Undergraduate (metric spaces)
A subset of a metric space is bounded if it is contained in some ball. A sequence or function is bounded if its set of values is bounded.