**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 $.