What is zero divided by infinity?

Answer 1

Zero divided by any number, rational or irrational, would still be zero.

---

However, division by infinity (or negative infinity) is not a defined operation. Although we can state that for any number a,

a/ ∞ = 0 and a/- ∞ = 0

this is not an actual value of zero, but a limiting value for a number that approaches ∞ . You can see that the reverse multiplication operation,

∞ x 0 = a

is only true in the single case where a = 0.

Answer 2

In ordinary math, no matter what the divisor, division of infinity is not defined.

Similarly, division by zero is not defined. Nothing, not even zero, can be rationally divided by zero. So division of infinity by zero cannot have a result.

(see the related question)