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\begin{itemize}
\item Composition of functions.
\item Composition of bijective, injective and surjective functions.
\item In $7, 77, 777, \ldots $ there is a number divisible by $1997$
  but not by $1995$ - use of divisibility, mod as an equivalence
  relation and pigeon-hole principle.
\item Bijection from $(0,1)$ to the reals.
\item Pigeonhole - any st of $101$ numbers from $1 .. 200$ contains
  $x$ and $y$ such that $x | y$.
\end{itemize}

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