What defines a line in geometric terms?

In geometric terms, a line is defined as having no thickness and extending infinitely in both directions. This concept emphasizes that a line is a one-dimensional figure, meaning it has length but no width or height. The idea of extending forever in both directions is crucial because it differentiates a line from line segments, which have defined endpoints and thus a finite length.

This characteristic allows mathematicians and geometricians to use lines in various applications, such as in the definition of geometric shapes, the calculation of slopes, and in forming equations. The notion of a line existing without thickness also implies that it cannot take up physical space, which is an essential aspect in geometry as it relates to other geometric entities such as planes and solid shapes.