What is Limit: Definition and 1000 Discussions

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




x

n




{\displaystyle x_{n}}
is denoted by





lim inf

n





x

n




or





lim
_



n






x

n


.


{\displaystyle \liminf _{n\to \infty }x_{n}\quad {\text{or}}\quad \varliminf _{n\to \infty }x_{n}.}
The limit superior of a sequence




x

n




{\displaystyle x_{n}}
is denoted by





lim sup

n





x

n




or





lim
¯



n






x

n


.


{\displaystyle \limsup _{n\to \infty }x_{n}\quad {\text{or}}\quad \varlimsup _{n\to \infty }x_{n}.}

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  1. C

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  2. A

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  3. L

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  8. S

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  11. Euge

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  12. Infrared

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  13. Euge

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  14. E

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  15. Mohmmad Maaitah

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  16. kornelthefirst

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  17. C

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  18. Lotto

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  19. C

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  20. ananonanunes

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  21. C

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  22. C

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  23. B

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  26. mcastillo356

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  27. G

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  28. Euge

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