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In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to", and is often denoted using the symbol (e.g., ). [1] If such a limit exists and is finite, the sequence is called convergent . [ 2 ]
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One can show that a convergent sequence has only one limit. The limit of a sequence and the limit of a function are closely related. On one hand, the limit as n approaches infinity of a sequence {a n} is simply the limit at infinity of a function a(n) —defined on the natural numbers {n}.
In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers.Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the ...
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This is a list of limits for common functions such as elementary functions. In this article, the terms a , b and c are constants with respect to x . Limits for general functions
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