A point B is said to lie between points A and C (where A, B, and C are distinct collinear points) if AB+BC=AC. A number of Euclid's proofs depend on the idea of betweenness without explicit mentioning it.

All points on a line segment excluding the endpoints lie between the endpoints.

Let P=(P,<=) be a partially ordered set, and let x,y,z in P. If x<=y<=z, then y is said to be between x and z. If x<=z in P and there is no y in P that is between x and z, then z covers x. Conversely, if z covers x, then no y is between x and z

See also

Collinear, Line Segment, Strictly Between

Portions of this entry contributed by Jim Loy

Portions of this entry contributed by Matt Insall (author's link)

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Cite this as:

Insall, Matt; Loy, Jim; and Weisstein, Eric W. "Between." From MathWorld--A Wolfram Web Resource.

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