Interval

Definition:

An interval is a range of numbers or values that lies between two specified endpoints.

Types of Intervals:

  1. Open Interval:

    2. An open interval does not include its endpoints. It contains all the values between the endpoints, but not the endpoints themselves. For example, the open interval (2, 7) consists of all real numbers greater than 2 and less than 7.

  2. Closed Interval:

    3. A closed interval includes both of its endpoints. It encompasses all the values between and including the endpoints. For example, the closed interval [0, 5] consists of all real numbers greater than or equal to 0 and less than or equal to 5.

  3. Half-Open or Half-Closed Interval:

    4. A half-open interval includes one endpoint but not the other. It includes the values greater than or equal to the first endpoint and less than the second endpoint (or vice versa). For example, the half-open interval [2, 6) consists of all real numbers greater than or equal to 2 and less than 6.

  4. Infinite Interval:

    5. An infinite interval extends indefinitely in at least one direction. It can either approach negative infinity, positive infinity, or both. For example, the infinite interval (-∞, ∞) or (-∞, +∞) includes all real numbers. Another example is the infinite interval (3, +∞), which includes all real numbers greater than 3.

  5. Bounded Interval:

    6. A bounded interval has finite values, meaning it has both a lower and an upper bound. The values within a bounded interval are limited and can be identified. For example, the bounded interval (1, 10) consists of all real numbers greater than 1 and less than 10.

  6. Unbounded Interval:

    7. An unbounded interval has at least one bound that extends to infinity. It does not have an upper or lower limit. For example, the unbounded interval (3, ∞) consists of all real numbers greater than 3, without any upper bound.