# Limit Point

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Related to Limit points: Accumulation point

## limit point

[′lim·ət ‚pȯint]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Limit Point

(or accumulation point). A limit point of a set A in a metric space is a point ξ in a space such that arbitrarily close to ξ there are points in A distinct from ξ. In other words, ξ is a limit point if any neighborhood of ξ contains an infinite number of points in A. A characteristic property of ξ is the existence of at least one sequence of distinct points of A that converges to ξ.

A limit point of a set does not have to belong to the set. Thus, every point on the real axis is a limit point for the set of rational points, because for every number—rational or irrational—we can find a sequence of distinct rational numbers that converges to it. Not every infinite set has a limit point; the set of integers, for example, lacks such a point. Every infinite bounded set of a Euclidean space, however, has at least one limit point.

### REFERENCE

Aleksandrov, P. S. Vvedenie v obshchuiu teoriiu mnozhestv i funktsil Moscow-Leningrad, 1948.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
A neutrosophic crisp point P [member of] [NCP.sub.n] in X is called a neutrosophic crisp limit point of B = < [B.sub.1], [B.sub.2], [B.sub.3] > iff every neutrosophic crisp open set containing P must contains at least one neutrosophic crisp point of B different from P.
It follows that [mathematical expression not reproducible], and hence both z and [M.sub.[lambda]]z are limit points of ([x.sub.n]).
These nonlinear resonance curves exhibit amplitude and frequency limit points. This indicates the existence of fold (saddle-node) bifurcations, which can only be mapped by the use of continuation techniques.
(d) Secant Poisson ratio (apparent incompressibility observed at limit point in compression).
= 2 max ({x - k | x is the limit point of A} [union] {0}).(14)
If the sets [??] and [??] have limit points in D, then the tuple [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is disk-cyclic on H.
Points [alpha] = 16.06 and [alpha] = 23.41 are limit points, where bifurcations are present.
The following lemma investigates some properties of the dense limit points.
For the case of two explanatory features, the categorization was given in the case of regular boundaries by L+1 limit points gi for feature A and K+ 1 limit points [h.sub.j] for feature B.
Then, the limit points of the zeros of the polynomials [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] are precisely the points of the line Re z = 1/2.
A set of points [LAMBDA} = [{[y.sub.n]}.sub.n[member of]Z] which has no limit points is called a set of sampling for the Hilbert space of [OMEGA]-bandlimited functions B([OMEGA]) if the norm squared of every bandlimited function is bounded above by the square sum of its samples taken on the points of [LAMBDA]:
With an increase in the inlet [C.sub.NO]/[C.sub.CO] ratio, the ignition temperature (temperature at which limit point observed), decreases.

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