How do I prove that half of length n is $\lceil\frac{n}{2}\rceil$

Question

Lets assume there are n objects, ordered in a list.

How do I prove that the first half (including the middle element) of length n is $\lceil\frac{n}{2}\rceil$?

And how do I prove that the last half (not including the middle element) of length n is $\lfloor\frac{n}{2}\rfloor$?

Thanks