In the following theorem, why does the limit end up being e from (14) and (15)? I thought we would need to show that the limsup and the liminf are equal to e for the limit to equal e?
2026-02-23 19:15:19.1771874119
Rudin 3.31 Why does the limit equal e?
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Since$$e\leqslant\liminf\nolimits_nt_n\leqslant\limsup\nolimits_nt_n\leqslant e,$$we have$$e=\liminf\nolimits_nt_n=\limsup\nolimits_nt_n,$$which is the same thing as asserting that $e=\lim_nt_n$.