Support function: Difference between revisions

Latest revision as of 15:17, 5 May 2014

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-A '''directed infinity''' is a type of infinity in the complex plane that has a defined angle ''θ'' but an infinite absolute value ''r''.<ref>{{MathWorld|urlname=DirectedInfinity|title=Directed Infinity}}</ref> For example, the limit of 1/''x'' where ''x'' is a positive number approaching zero is a directed infinity with angle 0; however, 1/0 is not a directed infinity, but a [[complex infinity]]. Some rules for manipulation of directed infinities are:
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-*<math>w\infty + z\infty = (w+z)\infty</math>
-*<math>z\infty = \frac{z}{\left | z \right |}\infty.</math>
-*<math>0\infty\text{ is undefined, as is }\frac{z\infty}{w\infty}</math>
-*<math>a z\infty = \begin{cases} z\infty & \text{if }a > 0, \\ -z\infty & \text{if }a < 0. \end{cases} </math>
-*<math>w\infty z\infty = (w z)\infty</math>
-== References ==
-{{reflist}}
-[[Category:Infinity]]
-{{math-stub}}

Support function: Difference between revisions

Latest revision as of 15:17, 5 May 2014

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