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Define intervals on the number scale?

Updated: 8/21/2019
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An interval on the number scale is a set of numbers between two end-point. Thus the closed interval [a, b] comprises all number between a and b as well as the two end points. An interval is open if neither end point is included, and semi-open (or semi-closed) if one end in included and the other is not.

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Q: Define intervals on the number scale?
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