Limit of a sequence: Difference between revisions
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The [[Mathematics|mathematical]] concept of '''limit of a sequence''' provides a rigorous definition of the idea of a sequence converging towards a point called the limit. | The [[Mathematics|mathematical]] concept of '''limit of a sequence''' provides a rigorous definition of the idea of a sequence converging towards a point called the limit. | ||
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[[if and only if]] for every [[real number]] ε > 0 there exists a [[natural number]] ''n''<sub>0</sub> such that for all ''n'' > ''n''<sub>0</sub> we have |''x''<sub>''n''</sub> − ''L''| < ε. The number ''n''<sub>0</sub> will in general depend on ε. | [[if and only if]] for every [[real number]] ε > 0 there exists a [[natural number]] ''n''<sub>0</sub> such that for all ''n'' > ''n''<sub>0</sub> we have |''x''<sub>''n''</sub> − ''L''| < ε. The number ''n''<sub>0</sub> will in general depend on ε. | ||
== See also == | |||
*[[Limit of a function]] | |||
*[[Limit (mathematics)]] | |||
Latest revision as of 09:45, 28 November 2007
The mathematical concept of limit of a sequence provides a rigorous definition of the idea of a sequence converging towards a point called the limit.
Suppose x1, x2, ... is a sequence of real numbers. We say that the real number L is the limit of this sequence and we write
if and only if for every real number ε > 0 there exists a natural number n0 such that for all n > n0 we have |xn − L| < ε. The number n0 will in general depend on ε.