From what I’ve seen, what seems to be the missing realization in some supporting theories, is the fact that no matter how large of a number you can deal with, no matter how high up the number line you can count or calculate, you will never see anything more than the infinitesimal small numbers at the beginning of the number line. I’ve read famous published math professors using terms like "as you approach infinity." The definition of ‘infinity’ is: ‘you can’t approach it.’

     When an electrician uses his Ohm meter to check a circuit for continuity, and the circuit is open, the needle on the meter will go to the high end of the scale. The open circuit will be referred to as "infinite resistance," or they will say "the needle went to infinity." The resistance of an open circuit isn’t really infinite, it’s just a very, very large number. The open circuit can still be shorted out by supplying a sufficiently high voltage. By using the term ‘infinity’ in a loose manner, it appears that the word itself has lost it’s meaning.

     Let’s imagine that I have an infinite railroad track. It would only have one end, i.e. the beginning. To be infinite, it could have no "other end." Now, suppose I have a special locomotive that has an infinite fuel supply and an engine that can accelerate forever. As the locomotive moves down the track, it gets faster and faster. The locomotive never stops going down the track, it never stops speeding up. No matter how fast it gets or how far it goes, it will never go beyond the infinitesimally small beginning of the track, and there will always be an infinitely long, never ending stretch of track that the locomotive will never, ever see, for the rest of forever. No matter how far you go toward infinity, it’s always just the beginning.

     Suppose I have two parallel lines that are separated by 1 meter. The lines are of infinite length and have no end points. Let’s suppose I rotate one of the lines so that it crosses the other line. If I rotate the line 180 degrees in ten seconds, I just touched every individual point indiviudually on an infinite line in a finite amount of time. At what distance from the point of rotation do the two lines separate from crossing and become parallel again? At what rate of acceleration does the point where the two lines cross, move away from the point of rotation? It can't be infinity, because infinity can't be reached. There is a point in time when they are crossed, and a next point when they are not. Sometimes infinity can be hard to figure out mathematically.

     There are different kinds of things that you can do, or can’t do with infinity. You can have two stationary points, point a and point b.. The distance between the two points cannot change. You can have a third point, point c, that always must remain in motion. Point c must always move away from point a, and always move toward point b, yet never arrive at point b. There are infinite series equations that can do this.

     I figured that if you had to prove Goldbach’s conjecture is true, you would have to find some mathematical connection between all prime numbers and all even numbers. It would have to be a connection that holds true for the entire number line. To prove Goldbach’s conjecture false, you could find the first even number that cannot be the sum of two primes, but this number may be far beyond humankind’s ability to calculate.

     We know that exactly 1/2 of the entire number line is made up of even numbers. Most mathematicians don’t need a proof to agree with this. But what about prime numbers? What is the exact ratio between prime numbers and composite numbers for the entire number line? By knowing this exact ratio, there might be a way to prove Goldbach right or wrong.