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An interval is a set of real numbers that includes all real numbers between one endpoint, , and another endpoint, . If both and are included in the interval, it is known as a closed interval, and if neither is included it is an open interval. If an endpoint is , then the interval is unbounded, otherwise, it is bounded.
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More
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Standard Interval Notation
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The standard interval notation is to write the endpoints of the interval separated by a comma, using round brackets to signify that the endpoint is not included, and square brackets to signify that it is. If an endpoint is , round brackets are used, since is not a real number, and cannot be included in an interval.
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Note: Since this is interval notation, and not an ordered pair, the brackets do not need to match: one endpoint may be included while the other is excluded. This is represented by closed and open brackets, respectively.
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Inequalities
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Intervals can also be represented by inequalities. The exclusion of an endpoint is represented by a strict inequality, or , and the inclusion of an endpoint is represented by or . When the interval is unbounded, the variable is restricted by only one or no inequalities. When the interval is bounded, the variable is restricted by two inequalities: one above, and one below.
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Graphical Representation
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When representing an interval graphically, a closed or solid point represents that the point is included, while an open point means that it is not included. This is demonstrated in the example below.
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Examples
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The closed interval from 3 to 4
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The open interval from -1 to
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The interval from -4 to -2, including -2, but excluding -4
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Standard Interval Notation
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Inequality
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Graphical Representation
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