If you divide by nothing, in one sense, you get nothing. In another sense, you are left with everything. However much there is to divide, all of it remains—undivided. The remainder is everything. To count it all, however, you must divide it up into discrete quantities.

Of course, you can keep dividing it into smaller and smaller parts, each of which is increasingly infinitesimal. As you do so, the number you are calculating approaches infinity.

This is the paradox of division by zero.

To conclude the process, you need to divide everything into parts that are equal to zero. That is, a point where there is no longer a quantity to enumerate. That is, where things cannot be divided further.

That point is zero, and at that point you have an infinite number of parts consisting of nothing.

Again, the longer you keep dividing—keep finding something to divide—the greater the number or divisions you must make. As long as you have something, you can theoretically keep dividing forever. Hence, the intuitive conclusion that division by zero equals infinity.

That is oddly consistent with the logical proposition that nothing is infinite.

Unfortunately, while we can all agree that multiplying any number by zero produces zero, it is a bit more controversial to suggest that any number divided by zero produces infinity. But take out a calculator and start dividing any number by smaller and smaller decimal numbers and see what happens. Soon enough, the implication becomes clear.

The smaller the number you use, the bigger the number you get.

Technically, division by zero is equivalent to a process of infinite division. Or dividing by infinity. But the main thing to remember is that zero is equal to nothing, and logical thought accepts the assertion that nothing is infinite.

Like infinity, zero is an imaginary number. We accept the irrationality of zero with any assumption of a discrete number of any kind. However many numbers you assign to count with, zero is implicitly included as the remaining quantity of any quantization.

It closes the circle, creating a finite set of things to account for everything. Like a circle, any base set of numbers falls within a loop describing an infinite spiral from zero to infinity.

Another way to look at it is that quantization is the creation of infinity.

To accomplish it, you merely need an inexhaustible supply of indivisible parts. Call them particles. Describe them as points in zero dimensions. Take them from something boundless, like empty space. Infuse them with the potential for everything. Give each one its own, unique value; individually, equal to any other: A discrete and uncompromised identity.

Though none of them possess any actual substance, everything is measured in terms of them, every thing being composed of them, gaining its own substance through them. This is possible because literally everything is divided between them.

Each one is too small to grasp with anything, so it is virtually impossible to deal with one in isolation. They are just too small to interact with, but everything is defined by their interactions with each other.

Everything, unquantifiable in their absence, becomes something that is shared by all of them. Their very existence depends on it. Just as the existence of everything is dependent on them. It is a relationship that makes existence possible.

And yet, we insist that division by zero is impossible.

Ironic.