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Questions and Answers
What is an open interval?
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?
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?
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?
What is a non-ending interval?
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Provide an example of a non-ending interval.
Provide an example of a non-ending interval.
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Provide an example of a half-open interval.
Provide an example of a half-open interval.
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Provide an example of an open interval.
Provide an example of an open interval.
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Provide an example of a closed interval.
Provide an example of a closed interval.
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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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