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2. Interval (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Interval_(mathematics)

   This characterization is used to specify intervals by mean of interval notation, which is described below. An open interval does not include any endpoint, and is indicated with parentheses. [2] For example, (,) = {< <} is the interval of all real numbers greater than 0 and less than 1.

3. Bracket (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Bracket_(mathematics)

   In some European countries, the notation [, [is also used for this, and wherever comma is used as decimal separator, semicolon might be used as a separator to avoid ambiguity (e.g., (;)). [ 6 ] The endpoint adjoining the square bracket is known as closed , while the endpoint adjoining the parenthesis is known as open .

4. Interval arithmetic - Wikipedia

   en.wikipedia.org/wiki/Interval_arithmetic

   The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.

5. Nested intervals - Wikipedia

   en.wikipedia.org/wiki/Nested_intervals

   4 members of a sequence of nested intervals. In mathematics, a sequence of nested intervals can be intuitively understood as an ordered collection of intervals on the real number line with natural numbers =,,, … as an index. In order for a sequence of intervals to be considered nested intervals, two conditions have to be met:

6. Interval order - Wikipedia

   en.wikipedia.org/wiki/Interval_order

   More formally, a countable poset = (,) is an interval order if and only if there exists a bijection from to a set of real intervals, so (,), such that for any , we have < in exactly when <. Such posets may be equivalently characterized as those with no induced subposet isomorphic to the pair of two-element chains , in other words as the ( 2 + 2 ...

7. Partition of an interval - Wikipedia

   en.wikipedia.org/wiki/Partition_of_an_interval

   A partition of an interval being used in a Riemann sum. The partition itself is shown in grey at the bottom, with the norm of the partition indicated in red. In mathematics, a partition of an interval [a, b] on the real line is a finite sequence x 0, x 1, x 2, …, x n of real numbers such that a = x 0 < x 1 < x 2 < … < x n = b.