Breaking Mathematics

There are several dimensions in math--the 0th, 1st, 2nd, 3rd, etc. dimensions. The most interesting one is the 0th dimension which is commonly referred to as a single point in space. A point has no dimension which means there is no measure. If you want to find the distance between two points, you will take the final point minus the initial point. For example, let's say that you want to find the distance between 6 and 2. All you have to do is this simple subtraction: 6-2 = 4. Now instead of finding the distance between two points, we want to find the distance of a single point. For example, we want to find the distance between 9 and 9. So all we have to do is 9-9 = 0. This is good that the definition of a point holds up to this example, but how does it hold up to the number line?

Between two points on a number line, there exists another point between the points. And this can go on towards infinity. So by definition there is an infinite amount of points that make up the number line. But we just proved that a point has no measure? So how does adding up infinite amount points make a measure? It's like adding zero an innumerable amount of times and miraculously appears a unit of measure.

The number line has a unique property. There is no way to determine what the next point is. For example, let's take the number four. The next number can be 4.01, but, actually, there is a number before 4.01 and that's 4.001. So in general, after each integer there is a number that has an infinite amount of zeros with the last number being 1 (i.e. 4.000000000...1). Therefore, between two points there is an infinite amount of points between those two points. Removing a single point from the number line will not affect any measure because there is no length removed, and there are an infinite amount of points that can take the missing point's place.

So drawing a point is impossible. By simply a dabbing a paper--ever so slightly--is still an exaggeration of what a point is. Also drawing graphs are impossible because they are composed of points.

This idea is part of number theory, and this topic almost broke math. Mathematicians ignored this idea and proceeded on doing math. This is a problem because all of mathematics is based on numbers and what they truly are. If this problem was not solved, all theorems, equations, and numbers, will be false. This naive notion of simply accepting the fact that numbers are numbers is horrible way to construct math.

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