Interval is a concept in mathematics which is used to describe the distance between two numbers or points. It is very helpful in solving problems related to distances, time, and other areas of mathematics. Intervals are also used in many scientific and engineering applications. This article will provide an overview of the concept of interval and its various applications.
Interval is defined as a bounded set of real numbers between two certain numbers. It is usually denoted by the letter “I”. The two endpoints of an interval are referred to as the lower bound and the upper bound. An interval can be denoted by a pair of numbers, such as [3, 7], which would represent all numbers between 3 and 7. An interval can also be denoted by a single number or symbol, such as (2, ∞), which would represent all numbers greater than 2.
Intervals are used in many scientific and engineering fields. In physics, intervals are used to measure distance, time, velocity, and acceleration. In mathematics, intervals are used to solve equations and to find the solutions of certain problems. In engineering, intervals are used to design and analyze systems.
Intervals can be classified in various ways. They can be open, closed, half-open, or half-closed. An open interval indicates that the two endpoints are not included in the interval, whereas a closed interval indicates that the two endpoints are included. A half-open interval indicates that the lower bound is included, but the upper bound is not, and a half-closed interval indicates that the upper bound is included, but the lower bound is not.
Intervals can also be classified according to their length. An interval of length 0 is referred to as a degenerate interval. An interval of length 1 is referred to as a point interval. An interval of length greater than 1 is referred to as a proper interval.
Intervals are also used to describe the size of sets. A set is said to be finite if it has a finite number of elements, and infinite if it has an infinite number of elements. Intervals can be used to describe the size of a set, as a set is said to be of length n if its elements can be represented by an interval of length n.
Interval is a useful concept that is used in many scientific and engineering fields. It is used to measure distances, solve equations, and find solutions to various problems. It is also used to classify sets according to their size.
References
Fowler, A. (2016). The Mathematics of Intervals. In J. C. Mason & M. C. Ercegovac (Eds.), Discrete Mathematics and its Applications (7th ed., pp. 78-86). New York, NY: McGraw-Hill Education.
Kreyszig, E. (2011). Advanced Engineering Mathematics (10th ed.). Hoboken, NJ: John Wiley & Sons.
Mason, J. C., & Ercegovac, M. C. (2016). Discrete Mathematics and Its Applications (7th ed.). New York, NY: McGraw-Hill Education.
Weisstein, E. W. (n.d.). Interval. Retrieved from http://mathworld.wolfram.com/Interval.html