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The process of extending a straight line segment is called production.

Such a straight line segment is said to be produced.

The line segment can be extended in either direction, thus producing an infinite half-line, or in both directions, thus producing an infinite straight line.

In the words of Euclid:

To produce a finite straight line continuously in a straight line.

(The Elements: Book $\text{I}$: Postulates: Euclid's Second Postulate)