The concept of zero and infinity

We always have had a hard time thinking about the concepts of zero and infinity. For example, what does it mean to divide an object into no parts? If we divide something into an infinite number of parts, then I'll imagine that each part will be infinitesimally small, so small that it would be nearly zero.

All this we know, but what about this: We know there are infinite number of real numbers between 0 to 1. Or between any 2 integers. The number line in essentially continuous. A point on such a line, then would not have any length, standard definition. It would not make sense for a point to have length. Yet it must, because an infinite number of points, each of zero length, suddenly makes a well-defined, measurable length. Lets do it in another way. Suppose we want to locate the point called '1.0000...' on the number line. We start by observing that this point we want to locate is somewhere between 0 and 2. Then we narrow our search to between 0.5 and 1.5. Then we can narrow somemore to 0.9 and 1.1. Or 0.9999 and 1.0001. We can continue to do this forever. Finally coming to 0.9999999... and 1.00....01. Effectively, we have reached the point we are locating. But we also notice that we can continue to do this indefinitely and still the point we are locating appears to have some sort of length.

This sort of continuity problem is striking the heart of space, time and matter. In short, all of physics. With the proposal of the 'atomos' idea, physics is starting to believe that ultimately the process of dividing and cutting must stop somewhere. Precisely where is unclear, it definitely is causing problems in understanding.

Perhaps 0 and infinity are the one and the same. Imagine a number line that instead of marching forever in 2 opposite directions in a straight line, it wraps around itself, joining negative infinity to positive infinity. Or perhaps if we allow 0 * infinity to equal to 1...

Somehow, everything is nothing, and if we accumulate enough of 'nothings', something will appear. We definitely need to revise our concept of zero and infinity.