Tipos de Intervalos.

Understanding Intervals in Inequalities

Introduction to Intervals

• The video introduces the concept of intervals, explaining their role in solving inequalities. An interval is defined as a set of numbers enclosed within rectangular or circular brackets.

Types of Intervals

• Two main types of intervals are discussed: closed intervals (where endpoints are included) and open intervals (where endpoints are excluded). Mixed intervals can also occur, combining both types.

Differences Between Interval Types

• Closed intervals indicate that the endpoints are part of the solution set, while open intervals signify that the endpoints do not belong to the solution. This distinction is crucial for understanding how solutions to inequalities are represented.

Example with Specific Values

• An example is provided using a set of numbers 1, 2, 3, 4, 5, 6, 7, 8, where 1 and 8 serve as the extremes. The left endpoint (1) is included in a closed interval while it would be excluded in an open interval.

Clarifying Solutions with Endpoints

• If an interval is expressed as [1,8), it indicates that while '1' is included in the solution set ('closed'), '8' is not ('open'). Thus, the actual solution range would be from '2' to '7', emphasizing how endpoint inclusion affects overall solutions.

Mixed Intervals Explained

• In mixed intervals like [1,8), '1' being included means it contributes to the solution while '8' does not. This highlights how different combinations affect what constitutes a valid solution for inequalities.