In mathematics, a sequence of nested intervals can be intuitively understood as an ordered collection of intervals I n {\displaystyle I_{n}} on the real...

The nested interval theorem is another form of completeness. Let In = [an, bn] be a sequence of closed intervals, and suppose that these intervals are...

we halve the length of an interval at each step, the limit of the interval's length is zero. Also, by the nested intervals theorem, which states that...

the nested intervals theorem, which guarantees that given a sequence of nested, closed intervals whose lengths become arbitrarily small, the intervals contain...

The nested set model is a technique for representing nested set collections (also known as trees or hierarchies) in relational databases. It is based...

specifically general topology, the nested interval topology is an example of a topology given to the open interval (0,1), i.e. the set of all real numbers...

inside it Nested intervals, in mathematics, intervals within intervals Nested variation or nested data, described at restricted randomization Nested case-control...

of nested intervals that excludes all the numbers in P and whose intersection contains a single real number in [a, b]. The sequence of intervals starts...

computer science, an interval tree is a tree data structure to hold intervals. Specifically, it allows one to efficiently find all intervals that overlap with...

Cantor's intersection theorem, also called Cantor's nested intervals theorem, refers to two closely related theorems in general topology and real analysis...

interval and an edge between vertices whose intervals intersect. It is the intersection graph of the intervals. Interval graphs are chordal graphs and perfect...

generalization of the bisection method in the complex plane Nested intervals Burden & Faires 2014, p. 51 "Interval Halving (Bisection)". Archived from the original...

be represented as the interval graphs for a set of nested intervals. A set of intervals is nested if, for every two intervals in the set, either the...

sets of unit intervals, or of properly nested intervals (intervals none of which contains any other one). Based on these two types of interval representations...

completeness axiom, such as the convergence of Cauchy sequences or the nested intervals theorem. The logical status of the property depends on the construction...

Visualizing a measure zero set as the limit of a sequence of nested intervals. Pages in "The Book of Sand" have measure zero....

cardinality greater than that of N. His proof used an argument with nested intervals, but in an 1891 paper, he proved the same result using his ingenious...

Fixed Point Theorem, so methods based on it do not work. Instead, nested intervals converge slowly but steadily. Recently, however, it has been shown...

Nested wells, also referred to as nested monitoring wells, are composed of multiple tubes or pipes, typically terminating with short screened intervals...

confidence interval is random (as it depends on the random sample). Bayesian credible intervals differ from frequentist confidence intervals by two major...

with any sequence of real numbers. Using this sequence, he constructs nested intervals whose intersection contains a real number not in the sequence. Since...

The nested sampling algorithm is a computational approach to the Bayesian statistics problems of comparing models and generating samples from posterior...

Nested RAID levels, also known as hybrid RAID, combine two or more of the standard RAID levels (where "RAID" stands for "redundant array of independent...

this sense, strictly larger than the set of natural numbers using a nested intervals argument. This result was later refined into the more widely known...

if it has a nested ear decomposition. Moreover, any open ear decomposition of a 2-vertex-connected series–parallel graph must be nested. The result may...

graphs are generalized by the trapezoid graphs. Systems of intervals in which no two are nested produce a more restricted class of graphs, the indifference...

The least-upper-bound property The greatest-lower-bound property The nested interval property The Bolzano-Weierstrass theorem The convergence of Cauchy...

topology on R Right half-open interval topology Nested interval topology Overlapping interval topology Interlocking interval topology Hjalmar Ekdal topology...

being broken out to; placing the nested loops in a function and using return to effect termination of the entire nested loop; or using a label and a goto...

Every decreasing nested sequence of nonempty closed subsets S1 ⊇ S2 ⊇ ... in (X, d) has a nonempty intersection. Every increasing nested sequence of proper...