Editing Projectively extended real line (section)

== Interval arithmetic ==
[[Interval arithmetic]] extends to <math>\widehat{\mathbb{R}}</math> from <math>\mathbb{R}</math>. The result of an arithmetic operation on intervals is always an interval, except when the intervals with a binary operation contain incompatible values leading to an undefined result.{{efn|For example, the ratio of intervals <math>[0,1]/[0,1]</math> contains {{math|0}} in both intervals, and since {{math|0 / 0}} is undefined, the result of division of these intervals is undefined.}} In particular, we have, for every <math>a, b \in \widehat{\mathbb{R}}</math>:
:<math>x \in [a, b] \iff \frac{1}{x} \in \left[ \frac{1}{b}, \frac{1}{a} \right] \!,</math>
irrespective of whether either interval includes {{math|0}} and {{math|∞}}.