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lim sup, the largest value a sequence returns to infinitely often.
Also known as: Limsup, Upper limit, Superior limit
Where an ordinary limit may fail to exist because a sequence oscillates, the limit superior always exists in the extended reals: it is the eventual ceiling of the sequence. That guarantee is why it appears throughout analysis where lim would be an unsafe assumption.
Denotes the eventual least upper bound of a sequence or function — the largest limit point.
Contexts: Mathematics
Always exists in the extended real numbers, including where the ordinary limit does not, which is the reason for the notation.
Contexts: Mathematics
Is sometimes written with a bar over lim, which means the same thing.
Contexts: Mathematics
The letters lim followed by sup, with a variable and an arrow set beneath, sometimes replaced by lim under a horizontal overbar.