"WM" <email@example.com> wrote in message news:firstname.lastname@example.org... > On 14 Jul., 20:01, "dilettante" <n...@nonono.no> wrote: >> "WM" <mueck...@rz.fh-augsburg.de> wrote in message >> news:email@example.com... >> > On 14 Jul., 18:38, "dilettante" <n...@nonono.no> wrote: >> >> >> "About that of which we cannot speak, we must remain silent." >> >> > That's why you are silent about mathematics, in this special case? >> >> > Mathematics, as I teach it gives the improper limit >> > ((((((10^0)/10)+10^1)/10)+10^2)/10)+... = oo >> > of the sequence >> >> > 1 >> > 0,1 >> > 10,1 >> > 1,01 >> > 101,01 >> > 10,101 >> > 1010,101 >> > 101,0101 >> > ... >> >> > Set theory gives 0. >> > What is correct? >> >> The limit is infinity. Set theory says nothing different, > > Set theory says the limit is less than 1, because for every digit > occuring left of the comma (the comma is taken from a German text, > here representing a decimal point) the step can be determined, when > this digit disappears right of the comma
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.
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.