An interval that is both open and closed is a set of real numbers that includes its endpoints and all the numbers in between, but does not include any numbers outside of the interval.
An interval that is both open and closed is typically represented using square brackets [ ] for closed intervals and parentheses ( ) for open intervals. For an interval that is both open and closed, the notation used is [ ).
An open interval does not include its endpoints, while a closed interval includes its endpoints. For example, the open interval (0, 1) includes all real numbers between 0 and 1, but does not include 0 or 1. The closed interval [0, 1] includes all real numbers between 0 and 1, including 0 and 1.
An interval that is both open and closed is important in mathematics because it allows for more precise and accurate calculations and descriptions of sets of real numbers. It also helps to avoid ambiguity in mathematical statements and proofs.
Yes, an interval that is both open and closed can be infinite. For example, the interval [0, ∞) includes all real numbers greater than or equal to 0, while the interval (-∞, ∞) includes all real numbers.