For the general mathematical concept, see Limit (mathematics).
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The sequence given by the perimeters of regular n-sided polygons that circumscribe the unit circle has a limit equal to the perimeter of the circle, i.e. . The corresponding sequence for inscribed polygons has the same limit.
1
0.841471
2
0.958851
...
10
0.998334
...
100
0.999983
As the positive integer becomes larger and larger, the value becomes arbitrarily close to . We say that "the limit of the sequence equals ."
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, the sequence is called convergent.[2] A sequence that does not converge is said to be divergent.[3] The limit of a sequence is said to be the fundamental notion on which the whole of mathematical analysis ultimately rests.[1]
Limits can be defined in any metric or topological space, but are usually first encountered in the real numbers.
^ abCourant (1961), p. 29.
^Weisstein, Eric W. "Convergent Sequence". mathworld.wolfram.com. Retrieved 2020-08-18.
^Courant (1961), p. 39.
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