On 15 Jul., 04:22, "dilettante" <n...@nonono.no> wrote: > "Virgil" <vir...@ligriv.com> wrote in message > > news:virgil-C28E88.firstname.lastname@example.org... > > > > > > > In article > > <732fa405-2987-4a12-9131-16256bc6c...@fi17g2000vbb.googlegroups.com>, > > WM <mueck...@rz.fh-augsburg.de> wrote: > > >> 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? > > >> > > Regards, WM > > >> > 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 > > >> Regards, WM > > > Quite correct, at least for any set theory generally accepted by > > standard mathematics. > > Good grief, Virgil. Do you really believe that the limit of the sequence 1, > .1, 10.1, 1.01, 101.01, 10.101, 1010.101, 101.0101 (or > ((((((10^0)/10)+10^1)/10)+10^2)/10)+... where the sequence is determined by > starting at the innermost parenthesis and performing one operation for each > term) something other than infinity? This is a sequence of numbers. It's > limit has nothing to do with vases or balls, or digits that supposedly cross > the decimal point (really - you think that the '1' to the immediate right of > the decimal point is somehow one of the particular '1's from the decimal > reprentation of the previous number on the list, and that this > identification has something to do with the limit of this sequence of > numbers?)
Dear Dilettante: First, the 1 and 0 can be indexed as the first, the second, the third, and so on. Second, instead of 1 and 0 you can use the indexes themselves: The limit of the sequence 21 2.1 432.1 43.21 6543.21 654.321 ... is not 0 but oo, in mathematics. http://www.hs-augsburg.de/~mueckenh/GU/GU12c.PPT#403,25,Folie 25 Third: I happened to publish § 077, by pure accident it gives just the opinion of a leading set theorist. Perhaps that will convice you. Fourth, from your mathematically healthy reaction I obtain that you are not among the lost souls of matheology. That fills my heart with joy.