Directed infinity

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A directed infinity is a type of infinity in the complex plane that has a defined complex argument θ but an infinite absolute value r.[1] For example, the limit of 1/x where x is a positive real number approaching zero is a directed infinity with argument 0; however, 1/0 is not a directed infinity, but a complex infinity. Some rules for manipulation of directed infinities (with all variables finite) are:

Here, sgn(z) = z/|z| is the complex signum function.

See also


  1. ^ Weisstein, Eric W. "Directed Infinity". MathWorld. 
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