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Proposition: Inequality between Powers of $2$ and Factorials
For all natural numbers $n\ge 4$, the following inequality holds $$2^n\le n!.$$
Example
For $n < 4$, we have
$$\begin{array}{rrcc}n&2^n&n !&\text{comparison}\\
0&1&1& = \\
1&2&1& > \\
2&4&2& > \\
3&8&6& > \\
\end{array}$$
Table of Contents
Proofs: 1
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983