> In reality there is not a d/2 for every d. The shortest possible wave > cannot be shortened and cannot be used to find a shorter d than its > wavelength or a finite fraction of it. Further, if the shortest > possible wave is created, there are no atoms marking a distance any > longer and no men to measure it, because all energy has been used to > create the wave. > > Regards, WM
Whether there is a physical distance of d/2 for every physical distance g is as irrelevant to mathematics as the undoubtable existence of a positive mathematical distance of d/2 for every positive mathematical distance d is irrelevant to physics.
WM may know a little physics, but he clearly knows considerably less about mathematics.
"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."