Betweenness

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Point B is between points A and C

Betweenness is the property of lines in certain geometries, such as plane geometry, which allows one to talk about when a third point is between two points.

Betweenness does not hold in some geometries such as non-Euclidean geometry and the Fano plane. Betweenness is equivalent to the line being a linear order of its points. The concept of betweenness was first mathematically expressed by David Hilbert[1], though the concept has naturally been used imprecisely in mathematics since at least the time of Euclid.

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