Limit of a sequence: Difference between revisions
Jump to navigation
Jump to search
imported>Igor Grešovnik m (added definition) |
mNo edit summary |
||
| (2 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
{{subpages}} | |||
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. | ||
| Line 7: | Line 8: | ||
[[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)]][[Category:Suggestion Bot Tag]] | |||
Latest revision as of 06:00, 12 September 2024
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.