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nodes/114/114.tex

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   \item \emph{monotonically decreasing} if for all $n\in\mathbb{N}$ holds $a_n\geq a_{n+1}$.
   \item \emph{strictly monotonically decreasing} if for all $n\in\mathbb{N}$ holds $a_n > a_{n+1}$.
 \end{enumerate}
+\end{Definition}
 
 We make essential use of Dedekind's theorem to prove the following result:
 \begin{Theorem}[Convergence of bounded and monotonic sequences]\label{thm:monbndseq}