If there is an infinite amount numbers from 1 to 2, how do we measure inches, meters, seconds, time, etc.? Or perhaps, 1 inch is infinite and...

This is an excellent question. First we make a distinction between a mathematical model and a physical model.

There are indeed an infinite number of real numbers between 0 and 1 on the real number line. Each number represents a mathematical point on the number line. But these numbers have no physical manifestation -- each point has no size (no length, width, nor height.) Even with the most powerful tools we have available, any "point"...

This is an excellent question. First we make a distinction between a mathematical model and a physical model.

There are indeed an infinite number of real numbers between 0 and 1 on the real number line. Each number represents a mathematical point on the number line. But these numbers have no physical manifestation -- each point has no size (no length, width, nor height.) Even with the most powerful tools we have available, any "point" we make takes up some finite volume in our three dimensional world.

In fact, it might not even make sense to speak of anything with spatial dimensions smaller than the Planck scale, as space might not exist at that scale.

So what do we mean by a measurement of 1 inch? If we say that something is 1 inch long, we are actually saying that it is somewhere between 1/2 and 3/2 inches long or `1/2 <= l < 3/2 ` . If we say that something is 1.0 inches, then we indicate that its length is between .99 and 1.05 inches, and so on. We must take into account the precision of the measurement device. In practice, for extremely delicate measurements we must use statistics to give the length.

So while we have a very precise definition of a second (as a number of vibrations of a cesium atom, etc...), this really represents a tiny range of values.