Wikipedia says that we need the axiom of choice to prove that Banach Limits exist: https://en.wikipedia.org/wiki/Banach_limit
Isn't the map $\limsup:l_\infty \to \mathbb{R}$ a Banach limit? Why would we then need the axiom of choice?
2026-03-25 12:55:23.1774443323
Isn't Limsup a Banach Limit?
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$\lim \sup$ is not linear so it is not a Banach limit.