Ecmandu wrote:Convergences add a magic infinitesimal to round off.

Untrue. It took 200 years, but mathematicians finally figured out how to banish that kind of imprecise thinking. The theory of limits is perfectly logically rigorous and does away with magic infinitesimals.

Ecmandu wrote:When dealing with infinity, the odds of picking the correct number (that an infinity number generator will pick, or bob next door) isn't 0.0...1. When it converges at infinity, the odds are exactly zero percent.

Untrue as I pointed out. You can't put a uniform distribution on a countable set. That's because of the axiom of countable additivity, explained in the probability link I gave you earlier. If the probability of picking each of 1, 2, 3, ... is zero, then the sum of those probabilities is zero. Yet the probability of picking SOME number is 1 as you noted. Therefore we can NOT put a uniform probability distribution on any countably infinite set.

Ecmandu wrote:Convergences work both ways, not only magically adding the infinitesimal, but subtracting it as well.

Simply not true. There are no magic infinitesimals in the real numbers.