CLOSED INTERVAL Meaning and
Definition
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A closed interval is a concept in mathematics that refers to a segment of the real number line that includes both of its endpoints. It is represented by enclosing the endpoints with square brackets, such as [a, b]. The first number, 'a', represents the left endpoint of the interval, while the second number, 'b', denotes the right endpoint.
In a closed interval, all the real numbers between 'a' and 'b', including 'a' and 'b' themselves, are included. This means that any value within this range is part of the closed interval. For instance, in the closed interval [2, 5], all real numbers from 2 to 5, 2 and 5 included, are part of the interval. The interval [2, 2] would only consist of the single element 2.
Closed intervals are important in calculus, analysis, and various other branches of mathematics. They are used to define functions, study continuous functions, determine convergence of sequences, and solve equations. By defining an interval as closed, mathematicians ensure that both endpoints are accounted for, making it easier to analyze and work with the set of values in between.
In conclusion, a closed interval is a set of real numbers that includes both of its endpoints, denoted by enclosing them with square brackets [a, b]. It is fundamental in mathematical analysis to study functions, sequences, and equations.
Common Misspellings for CLOSED INTERVAL
- xlosed interval
- vlosed interval
- flosed interval
- dlosed interval
- ckosed interval
- cposed interval
- coosed interval
- clised interval
- clksed interval
- cllsed interval
- clpsed interval
- cl0sed interval
- cl9sed interval
- cloaed interval
- clozed interval
- cloxed interval
- cloded interval
- cloeed interval
- clowed interval
Etymology of CLOSED INTERVAL
The etymology of the word "closed interval" can be traced back to the combination of the two individual words: "closed" and "interval".
The word "closed" comes from the Old French word "clos" which means "closed" or "enclosed". It ultimately derives from the Latin word "clausus" which carries a similar meaning of "shut" or "closed".
The word "interval" originates from the Latin word "intervallum", which refers to the space between two points or objects. It is composed of the prefix "inter-" meaning "between" and the word "vallum" meaning "rampart" or "wall".
When these two words are combined, "closed interval" refers to a mathematical term that represents a set of real numbers between two specified endpoints, where the endpoints themselves are included in the set.
Similar spelling words for CLOSED INTERVAL
