extended real numbers

The set R union {+∞, - ∞} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. Although the notation for this set is not completely standardized, R^_ is commonly used. The set may also be written in interval notation as [-∞, + ∞]. With an appropriate topology, R^_ is the two-point compactification (or affine closure) of R. The improper elements, the affine infinities +∞ and -∞, correspond to ideal points of the number line. Note that these improper elements are not real numbers, and that this system of extended real numbers is not a field.

compactification | indeterminate | limit | projectively extended real numbers | R | R^- | real number | R^+ | set closure