Interval Notation

Interval notation is a way of representing a set of numbers within a specified range. It is commonly used in mathematics to describe the possible values of a variable, the domain of a function, or the solutions to an inequality.

Types of Intervals

There are four main types of intervals:

1. Closed interval: [a, b] - includes both endpoints a and b
2. Open interval: (a, b) - does not include endpoints a and b
3. Half-open interval: [a, b) or (a, b] - includes one endpoint but not the other
4. Unbounded interval: (-∞, a), (a, ∞), (-∞, ∞) - extends indefinitely in one or both directions

Representation

In interval notation, the left endpoint of the interval is written first, followed by a comma, and then the right endpoint. For example:

• Closed interval from 1 to 5: [1, 5]
• Open interval from -3 to 2: (-3, 2)
• Half-open interval from 0 to 7: [0, 7)
• Unbounded interval from -∞ to 4: (-∞, 4)

Study Guide

When working with interval notation, it's important to understand the different types of intervals and how to represent them correctly. Here are some key points to remember:

• Identify whether the interval is open, closed, half-open, or unbounded.
• Determine the left and right endpoints of the interval.
• Write the interval using the appropriate notation, making sure to include the correct symbols (parentheses for open intervals, brackets for closed or half-open intervals).
• Pay attention to the direction of the interval (e.g., from smallest to largest number).

Practice representing different intervals in interval notation and interpreting given intervals to enhance your understanding of this concept.

Remember that interval notation provides a concise and standardized way to express ranges of numbers, making it a valuable tool in mathematical communication and problem-solving.