Editing Division by zero (section)

===Projectively extended real line===
The set <math>\mathbb{R}\cup\{\infty\}</math> is the [[projectively extended real line]], which is a [[one-point compactification]] of the real line. Here <math>\infty</math> means an unsigned infinity or [[point at infinity]], an infinite quantity that is neither positive nor negative. This quantity satisfies <math>-\infty = \infty</math>, which is necessary in this context. In this structure, <math>\frac{a}{0} = \infty</math> can be defined for nonzero {{math|''a''}}, and <math>\frac{a}{\infty} = 0</math> when {{math|''a''}} is not <math>\infty</math>. It is the natural way to view the range of the [[tangent function]] and cotangent functions of [[trigonometry]]: {{math|tan(''x'')}} approaches the single point at infinity as {{math|''x''}} approaches either {{math|+{{sfrac|π|2}}}} or {{math|−{{sfrac|π|2}}}} from either direction.

This definition leads to many interesting results. However, the resulting algebraic structure is not a [[Field (mathematics)|field]], and should not be expected to behave like one. For example, <math>\infty+\infty</math> is undefined in this extension of the real line.