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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.

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