Distance between infinitesimal and zero?

Solution 1:

In mathematics, ideas like “tiniest possible positive amount” and “next adjacent real point” don’t make sense.

Let’s suppose that we think $x$ is the smallest possible positive number. But then $x/2$ is even smaller, so $x$ wasn’t the smallest.

It’s really exactly the same situation as your clock hands: no matter how tiny a movement you make at the tip of the hand, a point half-way along the hand will move by an even smaller distance.

This is all in the idealized world of mathematics. In the physical world, there might be some smallest possible distance; I don’t know. Anyway, that’s a question for a physics forum, not here.