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
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=364)
(where
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=273)
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.