According to (26) on wolfram mathworld, one has
$$\sqrt{2\hspace{-0.04 in}\cdot \hspace{-0.04 in}\pi} \cdot n^{n+(1/2)} \cdot \operatorname{exp}((-n)\hspace{-0.02 in}+\hspace{-0.02 in}(1/((12\hspace{-0.04 in}\cdot \hspace{-0.04 in}n)\hspace{-0.02 in}+\hspace{-0.02 in}1)) \;\; < \;\; n!$$ and $$n! \;\; < \;\; \sqrt{2\hspace{-0.04 in}\cdot \hspace{-0.04 in}\pi} \cdot n^{n+(1/2)} \cdot \operatorname{exp}((-n)\hspace{-0.02 in}+\hspace{-0.02 in}(1/(12\hspace{-0.04 in}\cdot \hspace{-0.04 in}n)))$$
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However, I cannot find that page's Robbins reference anywhere, that page's link for the Feller reference points to amazon.com, and the only other thing from Feller that I could find on this topic just cites to Robbins for the bound. $\:$ How are the above two inequalities proven?