Search results
Results from the WOW.Com Content Network
Allen's interval algebra is a calculus for temporal reasoning that was introduced by James F. Allen in 1983.. The calculus defines possible relations between time intervals and provides a composition table that can be used as a basis for reasoning about temporal descriptions of events.
For example, the set of real numbers consisting of 0, 1, and all numbers in between is an interval, denoted [0, 1] and called the unit interval; the set of all positive real numbers is an interval, denoted (0, ∞); the set of all real numbers is an interval, denoted (−∞, ∞); and any single real number a is an interval, denoted [a, a].
A unit of time is any particular time interval, used as a standard way of measuring or expressing duration. The base unit of time in the International System of Units (SI), and by extension most of the Western world , is the second , defined as about 9 billion oscillations of the caesium atom.
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.
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:
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
In music theory, an eleventh is a compound interval consisting of an octave plus a fourth. A perfect eleventh spans 17 and the augmented eleventh 18 semitones , or 10 steps in a diatonic scale . Since there are only seven degrees in a diatonic scale, the eleventh degree is the same as the subdominant (IV). [ 1 ]
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.