Definition:Line/Straight Line Segment/Hilbert's Axioms

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Definition

Let $a$ be a line.

Let $A, B$ be points of $a$.

Then, $AB = \struct {a, A, B}$ is a segment.

A point $C$ lying on $a$ is said to be lying within the segment $AB$ if and only if $C$ is between $A$ and $B$.

The points $A$ and $B$ are the extremities of $AB$.

Al points lying on $a$ which are not in either of the above categories are lying outside the segment $AB$.

Sources

• 1902: David Hilbert: The Foundations of Geometry (translated by E.J. Townsend): $\text I \S 3$. Group $2$: Axioms of order