UnsignedInfinity

$${\tilde \infty}$$

Unsigned infinity. Generally used to represent $\lim_{z \to c} f(z)$ for functions where $\lim_{z \to c} \left|f(z)\right| = \infty$ but $\lim_{z \to c} \operatorname{sgn}\!\left(f(z)\right)$ is undefined.

$$\frac{1}{0}$$$${\tilde \infty}$$

UnsignedInfinity is the result of division by zero.

$$\left(\left|{\tilde \infty}\right|, \operatorname{sgn}({\tilde \infty})\right)$$$$\left(\infty, \operatorname{Undefined}\right)$$

UnsignedInfinity has infinite magnitude, but undefined sign.

$$\left(\infty {\tilde \infty}, {\tilde \infty} {\tilde \infty}\right)$$$$\left({\tilde \infty}, {\tilde \infty}\right)$$

Arithmetic involving infinities is well-defined when the limits are unambiguous

$$\left({\tilde \infty} + {\tilde \infty}, 0 {\tilde \infty}\right)$$$$\left(\operatorname{Undefined}, \operatorname{Undefined}\right)$$

Arithmetic involving infinities is undefined when the limits are ambiguous.

Last updated: 2020-03-06 00:22:16