That is by no means what I’m doing.

I start by assuming that time is infinite. Then I assume that the ball changes colors for all infinity. Then I assume that that ball must take time to change (how could something change in no time?). Next I assume that time is measurable (it has to be if any change is to occur). I acknowledge that when I measure this time, I am actually dividing the infinite quantity by a certain number to give me the measurement. But I realize, that infinity divided by any number, still yields infinity. If the time for the ball to change from one color to the next takes an infinite amount of time, then it would never reach the time for the change to occur. The only thing I envisioned was the most instantaneous switch of colors I could, in order to realize that even that took a certain amount of time. Everything else is purely mathematics.
This is exactly the problem. How do you divide infinity in such a manner as to get n equal amounts of 10 seconds? Every time you measure time, you are implicitly dividing all of time into equal parts of which have the same exact measurement which you measured. Following this, if time were infinite, the time for each change would also have to be infinite, which means that the change would never occur.
There are certain things in math that are present for idealistic simplification. For example, negative numbers do exist in math, but they don’t
physically exist. The same could be said of infinity in a sense. But still, let us assume that infinity with certainty exists in the physical world. The distance between 10 infinity (which is simply infinity) and 5 infinity (which is also simply infinity) is infinity. If the distance between 10 infinity and 5 infinity is infinite, how do you get from one to the other?