VTRMC 2004 Problem 6

An enormous party has an infinite number of people. Each two people either know or don't know each other. Given a positive integer $n$ , prove there are $n$ people in the party such that either they all know each other, or nobody knows each other (so the first possibility means that if $A$ and $B$ are any two of the $n$ people, then $A$ knows $B$ , whereas the second possibility means that if $A$ and $B$ are any two of the $n$ people, then $A$ does not know $B$ ).