Division by ∞

 Economics exists because the resources are finite (limited) but the needs infinite. 

Assume $A$ to be the finite set of all apples on earth. We want to divide this set by infinity, that is

$$\frac{A}{\infty},$$

which is undefined so far. Yet, there is a vague tendency of the mind to say 

$$\boxed{\frac{A}{\infty}\equiv\big\{\exists V:A\to\mathbb{R}\big\}}$$

where we call $V$ the Value function.

Then, every person's Share $S$ would be

$$S=\frac{C}{V},$$ where $C$ is the Capital of the person.