projectively extended real line

In real analysis, the projectively extended real line (also called the one-point compactification of the real line, or simply real projective line), is the extension of the number line by a point denoted . It is thus the set (where is the set of the real numbers), sometimes denoted by The added point is called the point at infinity, because it is considered as a neighbour of both ends of the real line. More precisely, the point at infinity is the limit of every sequence of real numbers whose absolute values are increasing and unbounded.