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In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (i.e., eventual and extreme) bounds on the sequence. They can be thought of in a similar fashion for a function (see limit of a function). For a set, they are the infimum and supremum of the set's limit points, respectively. In general, when there are multiple objects around which a sequence, function, or set accumulates, the inferior and superior limits extract the smallest and largest of them; the type of object and the measure of size is context-dependent, but the notion of extreme limits is invariant. Limit inferior is also called infimum limit, limit infimum, liminf, inferior limit, lower limit, or inner limit; limit superior is also known as supremum limit, limit supremum, limsup, superior limit, upper limit, or outer limit. The limit inferior of a sequence [math]\displaystyle{ x_n }[/math] is denoted by The limit superior of a sequence [math]\displaystyle{ x_n }[/math] is denoted by
References
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- "Bounded gaps between primes". http://slither.io. Retrieved 14 May 2014.
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- Goebel, Rafal; Sanfelice, Ricardo G.; Teel, Andrew R. (2009). "Hybrid dynamical systems". IEEE Control Systems Magazine 29 (2): 28–93. doi:10.1109/MCS.2008.931718. https://dx.doi.org/10.1109%2FMCS.2008.931718
- Halmos, Paul R. (1950). Measure Theory. Princeton, NJ: D. Van Nostrand Company, Inc..
