Directed infinity
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
- Point at infinity
References
- ^ Weisstein, Eric W. "Directed Infinity". MathWorld.
- v
- t
- e
Infinity (∞)
- Ananta (infinite)
- Apeiron
- Controversy over Cantor's theory
- Galileo's paradox
- Hilbert's paradox of the Grand Hotel
- Infinity (philosophy)
- Paradoxes of infinity
- Paradoxes of set theory
- Complex analysis
- Internal set theory
- Nonstandard analysis
- Set theory
- Synthetic differential geometry
- 0.999...
- Absolute infinite
- Actual infinity
- Aleph number
- Beth number
- Cardinal numbers
- Cardinality of the continuum
- Dedekind-infinite set
- Directed infinity
- Division by zero (Complex infinity)
- Epsilon number
- Gimel function
- Hilbert space
- Hyperreal numbers
- Infinite set
- Infinitesimal
- Ordinal numbers
- Point at infinity
- Regular cardinal
- Sphere at infinity (Kleinian group)
- Supertask
- Surreal numbers
- Transfinite numbers
This mathematical analysis–related article is a stub. You can help Wikipedia by expanding it. |
- v
- t
- e