Finite but unbounded set? I have come across an exercise sheet for my analysis class with the following instructions
In each of the cases below, either (i) give an example with the properties indicated or (ii) show that there is no example that has the properties indicated. Support each answer with a clear and concise mathematical argument.
One of the cases is 
A finite set $S \subseteq \mathbb R $ which is unbounded.
Can such a set exist, and if so any examples? Or am I right in presuming an unbounded subset cannot be finite?

The reals are a totally ordered set. Any subset of a totally ordered set is totally ordered. A finite subset S of the reals is totally ordered and therefore (being finite) has a first and last element f and l with the property that $f \le x \le l$ for all x in S. So S is bounded by f and l.
