open interval (Meaning)
Wordnet
open interval (n)
an interval that does not include its endpoints
Synonyms & Antonyms of open interval
No Synonyms and anytonyms found
open interval Sentence Examples
- In mathematics, an open interval denotes a range of real numbers that does not include its endpoints.
- The set of all real numbers between 0 and 1 forms an open interval, denoted as (0, 1).
- Graphically, an open interval is represented by an unfilled circle at each endpoint on a number line.
- The interval (a, b) is considered open if a < x < b for all x within the interval.
- Calculus often deals with functions defined over open intervals to study their behavior.
- The solution set for an inequality like 3 < x < 7 forms an open interval between 3 and 7.
- Engineers often analyze systems over open intervals of time to understand dynamic behavior.
- The concept of an open interval is fundamental in understanding limits and continuity in calculus.
- An open interval excludes its endpoints, distinguishing it from a closed interval.
- When discussing domains and ranges in functions, it's essential to consider whether intervals are open or closed.
FAQs About the word open interval
an interval that does not include its endpoints
No synonyms found.
No antonyms found.
In mathematics, an open interval denotes a range of real numbers that does not include its endpoints.
The set of all real numbers between 0 and 1 forms an open interval, denoted as (0, 1).
Graphically, an open interval is represented by an unfilled circle at each endpoint on a number line.
The interval (a, b) is considered open if a < x < b for all x within the interval.
