What does a parenthesis signify in interval notation?

In interval notation, parentheses are used to indicate an exclusive boundary. This means that the endpoints of the interval are not included in the set of values represented by the interval. For example, if an interval is denoted as (a, b), it represents all the numbers greater than a and less than b, but does not include the values a and b themselves.

This concept is particularly important in mathematical contexts involving inequalities or ranges of values, as it defines the limits within which certain properties hold true. Understanding the use of parentheses helps to accurately interpret and convey intervals, ensuring clarity in mathematical communication.

On the other hand, square brackets are used in interval notation for inclusive boundaries, indicating that the endpoints are part of the interval. Recognizing the distinction between these notations is essential for correctly stating the nature of the set being described.