# Bounded Intervals

Icebreaker
"If I and J are bounded, then I$$\cap$$J is also bounded."

Now, I was able to do this using the definition of suprema and infima and so fourth, but it is one godawful mess. I could sumbit it as is, but I was wondering if there's an easier way.

Let C be an upper bound of I, and D an upper bound of J. Then max{C, D} is an upper bound of $$I \cap J$$. Similarly for the lower bound.