On 15 Jul., 02:03, "LudovicoVan" <ju...@diegidio.name> wrote:
> > That remains invalid reasoning, a paralogism that simply does not model the > problem: a sensible statement would be that for every digit that goes to the > right 2 more are added on the left, so that never all digits are on the > right.
Infinity is tow-sided. A) We can reach every number n when counting from 1 to n. B) There remains always a number m outside of what we have counted, how big ever n may be.
That makes infinity impossible to deal with in a consistent mathematics. Matheologians simply suppress B and rely on A only. Therefore matheology yields inconsistent reults, as becomes obvious when considering B, as you did it here.
> Then, I have checked the definitions of limit inferior and superior: I can > see a problem when said limits are defined in terms of unions of > intersections and vice versa (entirely due to my limited understanding), > although it is apparent that the two limits must diverge, period.
If the definitions of set theory are applied, then they are both empty. (For instance, there is no natural number that is always in the set M_n.)