I was wondering why epsilon, the smallest positive number, isn't a rational number. I was watching a video a few days ago about surreal numbers, and I've learned that, in the field of surreal numbers, o.(9) is not equal to 1, in contrast to the field of the real numbers, where they represent the same number. In the field of surreal numbers, you would get epsilon by subtracting 0,(9) from 1. If you were to do this in the rationals, you would just get 0. But I think there is a method do get epsilon even in the rationals, you would just take the following limit:
limn→[infinity]n∑i=0110i
