Support function

A directed infinity is a type of infinity in the complex plane that has a defined angle θ but an infinite absolute value r. 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:

• $w\mathrm{\infty }+z\mathrm{\infty }=(w+z)\mathrm{\infty }$
• $z\mathrm{\infty }=\frac{z}{\left|z\right|}\mathrm{\infty }.$
• $0\mathrm{\infty }\text{ is undefined, as is }\frac{z\mathrm{\infty }}{w\mathrm{\infty }}$
• $az\mathrm{\infty }=\{\begin{array}{ll}z\mathrm{\infty }& \text{if }a>0,\\ -z\mathrm{\infty }& \text{if }a<0.\end{array}$
• $w\mathrm{\infty }z\mathrm{\infty }=(wz)\mathrm{\infty }$

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

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