Infinity

Input: Infinity

$$\infty$$

Positive infinity.

Input: -Infinity

$$-\infty$$

Negative infinity.

Input: Exp(ConstI / 3) * Infinity

$${e}^{i / 3} \infty$$

Infinity with a complex direction.

Symbolic evaluation examples

Input: Tuple(Infinity + (3 + 4*ConstI), ConstI * Infinity - 5, 2 * ConstI * Infinity)

$$\left(\infty + 3 + 4 i, i \infty - 5, 2 i \infty\right)$$

Output: Tuple(Infinity, Mul(ConstI, Infinity), Mul(ConstI, Infinity)) (evaluated by pygrim in 0.0102 s)

$$\left(\infty, i \infty, i \infty\right)$$

Infinities absorb complex numbers

Input: Tuple(Infinity + Infinity, Infinity * Infinity, (-Infinity) + (-Infinity))

$$\left(\infty + \infty, \infty \infty, -\infty + \left(-\infty\right)\right)$$

Output: Tuple(Infinity, Infinity, Neg(Infinity)) (evaluated by pygrim in 0.0015 s)

$$\left(\infty, \infty, -\infty\right)$$

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

Input: Tuple(Infinity - Infinity, Infinity / Infinity, 0 * Infinity)

$$\left(\infty - \infty, \frac{\infty}{\infty}, 0 \infty\right)$$

Output: Tuple(Undefined, Undefined, Undefined) (evaluated by pygrim in 0.0011 s)

$$\left(\operatorname{Undefined}, \operatorname{Undefined}, \operatorname{Undefined}\right)$$

Arithmetic involving infinities is undefined when the limits are ambiguous.

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