As one very, very basic example, consider the following question: What’s the next number larger than 0? Suppose I claimed I had such a number. Call it x. If we take x and divide it by 2, we have a number that’s even closer to 0. From this, we conclude there’s no next larger number than 0.
Now consider the following experiment. Take a piece of paper and put two points on it. Label one point 0 and the other point 1. Now imagine a line segment connecting the two points. We can associate each point on the line segment with a number between 0 and 1. One-half would correspond to the point halfway between 0 and 1, one-tenth would correspond to the point one-tenth of the way from 0 to 1, and so on.
Suppose we now draw the line segment. As we start to draw, we must leave the point 0, and in doing so the pencil must pass over a next point on the line segment – the next number larger than 0. But it doesn’t, because there is no next number larger than 0. How can that be?