# Math Help - analysis help

1. ## analysis help

Any ideas? Thanks!

Let I be a bounded interval. Prove that the intersection of I and Z is a finite set.

2. Originally Posted by friday616
Any ideas? Thanks!

Let I be a bounded interval. Prove that the intersection of I and Z is a finite set.
Maybe I'm taking some theorems for granted, here, which you are not permitted to do. However, I would say simply, as follows:

Since $I$ is bounded, then so too is $I\cap\mathbb{Z}$ bounded. Thus $|I\cap\mathbb{Z}|=1+\sup(I\cap\mathbb{Z})-\inf (I\cap\mathbb{Z})$.