I know that is has to be bounded because its finite, but I'm guessing there is some sort of mathematical proof for this?
What Drexel28 is trying to say is...
Assume that is finite but not bounded above.
Set but then the set is bounded by
Therefore, there must be some but then the set is bounded by ... ad infinitum.
The set must be infinite to be unbounded.
A similar argument shows the set is bounded below...