1. Let's understand the problem: find the value of $0 \div \infty$ where $\infty$ denotes infinity. 2. Division by infinity is a limit concept; it isn't a standard arithmetic operation. 3. Intuitively, dividing zero by an infinitely large number means: how many times does $\infty$ fit into 0? 4. Mathematically, we express this as a limit: $$\lim_{x \to \infty} \frac{0}{x}$$ 5. Since the numerator is zero, this fraction is always zero regardless of $x$ (except when $x=0$ which is undefined). 6. Therefore, $$\lim_{x \to \infty} \frac{0}{x} = 0$$. 7. Hence, the value of $0 \div \infty$ can be interpreted as 0. Final answer: $0$