Which of the following best defines a line?

A line is defined mathematically as a one-dimensional figure that extends indefinitely in both directions without any endpoints. This characteristic captures the essence of a line as it has length but no width or depth. It represents a continuous path of points in space where each point is defined by its position on the line.

In contrast, the other descriptions relate to different geometric shapes. For instance, a two-dimensional figure that is closed refers to shapes like circles or polygons, which enclose a space. The idea of a set of points extending in a single direction aligns more closely with a ray, which has a starting point and extends infinitely in one direction but does not represent the full definition of a line. Lastly, a figure with length and width but no depth describes a two-dimensional shape, such as a rectangle or square, distinct from the infinite and one-dimensional nature of a line.