Knowra Interval (mathematics) Interval (mathematics) A subset of the real line that contains every real number between any two of its points. Intervals may include or exclude their endpoints, and may be bounded or unbounded.
Real number : A number represented by a point on the continuous number line, including rational and irrational numbers. Intervals are subsets of the real numbers, ordered along the number line.
Interval union : The union of sets, containing every element that belongs to at least one of them. Overlapping intervals can unite into a larger interval; separated ones cannot.
Interval arithmetic : Arithmetic that computes enclosures of values using intervals instead of single numbers. It propagates bounded uncertainty through numerical calculations.
Discrete set : A set whose points are isolated from one another in its inherited topology. Intervals contain all points between members, unlike scattered collections of isolated points.
Order relation : A relation that compares elements using properties such as less than, greater than, or equality. The between-points condition is defined through the real numbers’ order.
Interval intersection : The intersection of sets, containing elements shared by all sets involved. The intersection of intervals is either another interval or the empty set.
Interval estimation : A statistical method that estimates a parameter by reporting a range of plausible values. Confidence intervals are a major statistical use of interval-shaped sets.
Rational numbers : Numbers expressible as a ratio of integers with nonzero denominator. A rational interval can omit irrational points, so it is not an interval in the real line.
Open interval : An interval that excludes both endpoints, such as (a,b) for real numbers a<b. It is one endpoint convention for specifying an interval.
Convex set : A set in a real vector space that contains every line segment joining any two of its points. Intervals are exactly the convex subsets of the real line.
Show all 23