Set of projectively extended real numbers

The set of projectively extended real numbers is a set containing the real numbers, as well as a new element $$\infin$$ which is at both ends of the number line. It corresponds to the real projective line because the vertical line going upwards (slope of $$+\infin$$)and the vertical line going downwards (slope of $$-\infin$$) both have the same gradient. It can be thus be constructed from the set of extended real numbers by identifying $$+\infin$$ and $$-\infin$$.