1. The problem asks for the value of $1 \div \infty$ where $\infty$ represents infinity. 2. Infinity is not a regular number; it is a concept representing an unbounded value that grows without limit. 3. When dividing 1 by an infinitely large number, the result approaches zero because the denominator becomes extremely large. 4. Formally, we write this limit as $$\lim_{x \to \infty} \frac{1}{x} = 0$$ which means as $x$ grows larger and larger without bound, $\frac{1}{x}$ gets closer and closer to zero. 5. Therefore, $1 \div \infty$ is considered to be $0$ in the sense of limits and infinitesimals.