Show that a nonempty finite subset of the Real Numbers has both a maximum and minimum.

I know I can use induction to solve this but I seem to be having some problems getting started:

Let P(n) be assertion: a nonempty finite subset of R has a max and min

P(1) is the assertion: a set S={1} has a max and min, both of which are 1.

Suppose P(k) is true for: a set S={k} containing a max and min.

Show P(k+1) true for S={k+1}

This is where I seem to be getting stuck. I am just not sure what to do from here (or even if my set up is correct)

Any help would be greatly appreciated!

Thank you