Question Number 219887 by SdC355 last updated on 03/May/25
$$\mathrm{what}\:\mathrm{is}\: \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\uparrow\uparrow^{\infty} =?? \\ $$$${a}\uparrow\uparrow^{{m}} =\underset{{m}\:\mathrm{times}} {\underbrace{{a}^{{a}^{{a}^{{a}^{\iddots} } } } }}\:\:\left(\mathrm{aka}\:\mathrm{Knuth}'\mathrm{s}\:\mathrm{up}\:\mathrm{notation}\right) \\ $$
Answered by MrGaster last updated on 03/May/25
$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\uparrow\uparrow^{\infty} =\mathrm{1} \\ $$