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Interval Notation Concepts

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Questions and Answers

What is an open interval?

An interval where the endpoints are NOT included. (correct)

An interval in which one endpoint is included but not the other.

An interval that contains its endpoints.

An interval that is expressed as 'infinity'.

What is a closed interval?

An interval where the endpoints are NOT included.

An interval expressed as '(-infinity, x]'.

An interval that contains its endpoints. (correct)

An interval that is partially composed of infinity.

What defines a half-open interval?

One endpoint is included, and the other is not. (correct)

Neither endpoint is included.

Both endpoints are included.

Infinity is part of the interval.

What is a non-ending interval?

An interval that approaches infinity which is expressed as open. Signup and view all the answers

Provide an example of a non-ending interval.

(-infinity, x] Signup and view all the answers

Provide an example of a half-open interval.

(1, infinity) Signup and view all the answers

Provide an example of an open interval.

(1, 5) Signup and view all the answers

Provide an example of a closed interval.

[1, 5] Signup and view all the answers

Study Notes

Interval Notation Concepts

Open Interval: Endpoints are not included, represented as (a, b).
Closed Interval: Includes both endpoints, denoted by brackets such as [a, b].
Half-Open Interval: One endpoint is included while the other is not, illustrated as [a, b) or (a, b].
Non-ending Interval: Expressed with infinity; infinity is always treated as an open endpoint.

Examples of Interval Notation

Non-ending Interval Example: Illustrated as (-∞, x] showing an interval that extends indefinitely to the left but includes x.
Half-Open Interval Example: (1, ∞) showcases an interval that starts at 1 (not included) and goes indefinitely towards positive infinity.
Open Interval Example: (1, 5) represents an interval that excludes both endpoints, covering all values between 1 and 5.
Closed Interval Example: [1, 5] indicates that both endpoints are included, encompassing all numbers from 1 to 5 inclusive.

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Description

Test your understanding of interval notation with this quiz. Explore different types of intervals, including open, closed, and half-open intervals, along with examples illustrating their meanings. Perfect for students learning about mathematical intervals.