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lim inf, the smallest value a sequence returns to infinitely often.
Also known as: Liminf, Lower limit, Inferior limit
The limit inferior is the eventual floor of a sequence, the mirror of the limit superior. A sequence converges precisely when its limit inferior and limit superior agree, which turns a question about convergence into a comparison of two quantities that always exist.
Denotes the eventual greatest lower bound of a sequence or function — the smallest limit point.
Contexts: Mathematics
Together with the limit superior gives a convergence test: the ordinary limit exists exactly when the two are equal.
Contexts: Mathematics
The letters lim followed by inf, with a variable and an arrow set beneath, sometimes replaced by lim under a horizontal underbar.