Or does it bother you, Allan, that Hofstadter's butterfly is a Cantor set, yet it can be measured in a physical laboratory? ( see also: https://www.youtube.com/watch?v=1JdS-1-yYu8 , also at times 1:03:00 and 1:09:00 ) Another quandry is that Rationals Q are dense in R, yet measure zero. Practically speaking, a numerical integral on the unit interval [0,1] is usually taken over a Q subset (precision-limited decimals), but we have already said that such a set "contributes nothing"! See for example: In[]:= Total[Table[N[Sin[Pi/2*RandomInteger[{0, 1000000}]/1000000 ]*Pi/2], {1000000}]]/1000000 Out[]:=1.00058 --Brad On Thu, Aug 8, 2019 at 3:30 AM Allan Wechsler <acwacw@gmail.com> wrote:
Does it bother you, Brad, that if S is a Cantor set in R, card (S) = card (R) but S is measure zero in R?