On 21 Nov., 14:10, William Hughes <wpihug...@gmail.com> wrote: > It is not enough to > give a an infinite process and declare a limit.
But it is enough to to consider the following sequence > >> > 01. > >> > 0.1 > >> > 010.1 > >> > 01.01 > >> > 0101.01 > >> > 010.101 > >> > 01010.101 > >> > 0101.0101 > >> > ... to see that it has the (improper) limit (((?((((((10^0)/10)+10^1)/10)+10^2)/10)+? )+10^n)/10)+? infinite. . And it is as easy to see that in set theory the set of indices left of the decimal point > >> > 0_2 1_1 . > >> > 0_2 . 1_1 > >> > 0_4 1_3 0_2 . 1_1 > >> > 0_4 1_3 . 0_2 1_1 > >> > 0_6 1_5 0_4 1_3 . 0_2 1_1 > >> > 0_6 1_5 0_4 . 1_3 0_2 1_1 > >> > 0_8 1_7 0_6 1_5 0_4 . 1_3 0_2 1_1 > >> > 0_8 1_7 0_6 1_5 . 0_4 1_3 0_2 1_1 > >> > ... has limit { }.
And it is further easy to know, that decimal fractions as conceived by Simon Stevinus cannot contain numerals without indices, even if no one does see them because they were not explicitly written.
