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Nondegenerate Interval

A nondegenerate interval is an interval containing more than one point. In particular, a bounded interval with finite endpoints a and b is nondegenerate when a<b, or equivalently when its length b-a is positive. The definition applies to open intervals, closed intervals, and half-closed intervals.

By contrast, the closed interval [a,a]={a} is a degenerate interval. When the endpoints coincide, the intervals (a,a), [a,a), and (a,a] are empty, and hence equal to emptyset.

See also

Closed Interval, Degenerate, Empty Set, Endpoint, Half-Closed Interval, Interval, Open Interval, Point

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Cite this as:

Weisstein, Eric W. "Nondegenerate Interval." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NondegenerateInterval.html

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