Mastering Interval Notation | A Concise Guide to Representing Ranges of Real Numbers

interval notation

Interval notation is a way to represent intervals, or sets of numbers, using brackets and parentheses

Interval notation is a way to represent intervals, or sets of numbers, using brackets and parentheses. It simplifies expressing ranges of real numbers in a concise and standardized format. Intervals can be closed or open, meaning whether or not the endpoints are included in the set. There are four types of interval notation:

1. Closed Interval: [a, b]
A closed interval includes both endpoints a and b. It represents all real numbers between a and b, including a and b themselves. The notation [a, b] is used to denote a closed interval.

For example, the interval [2, 5] represents the set of numbers 2, 3, 4, and 5.

2. Open Interval: (a, b)
An open interval does not include the endpoints a and b. It represents all real numbers between a and b, not including a and b themselves. The notation (a, b) is used to denote an open interval.

For example, the interval (2, 5) represents the set of numbers between 2 and 5, but does not include 2 or 5.

3. Half-Open or Half-Closed Interval: [a, b) or (a, b]
A half-open or half-closed interval includes one endpoint but not the other. It represents all real numbers between a and b, including or excluding one endpoint. The notation [a, b) or (a, b] is used for half-open or half-closed intervals.

For example, the interval [2, 5) represents the set of numbers 2, 3, and 4, but not 5.

4. Unbounded Interval: (-∞, ∞)
An unbounded interval represents the set of all real numbers. It does not have any specific endpoints. The notation (-∞, ∞) is used to denote an unbounded interval.

For example, the interval (-∞, ∞) represents the set of all real numbers.

In interval notation, square brackets [ ] indicate that the endpoint is included, while parentheses ( ) indicate that the endpoint is excluded.

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