An open curve
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A Line ;)
A straight line is formed when we join two points say A and B. These both points are called the end-points
The term you are looking for is "line." In geometry, a line is a one-dimensional figure that extends infinitely in both directions. It is composed of an infinite number of points and has no endpoints.
The set of points on a straight curve that extends to infinity in both directions is a line. A ray is the set of points that lie on a straight curve that is terminated at a point, and continues to infinity. It is also called a half-line. If the set is terminated at a point at both ends, then it is a line segment.
No, just the opposite: A line segment has two end points. The word line is usually used to refer to a line segment, but by the mathematical definition, a line extends forever in both directions. (A line that has one end point and extends forever in one direction is called a ray.)