Anonymous asked:Lexy I am in a kerfuffle that humans must confound the number 0.999999999... and all that to a boring 1. With your non-human intellect and experience with technical doohickeys, at what scale would you start to consider something "too small" (like say, atomic-size or whatnot)?
I fail to see the connection between these sentences. 0.9̅ and 1 are different expressions of the same value, much the way 0.5 and ½ are. Mathematicians love nothing more than choice, assuming they can agree that such a thing exists.
Thus the difference between the two numbers is zero, which is certainly an appropriate lower bound for any notion of “too small”. Beyond that, context is everything: while a grain of sand is certainly not large enough to weigh down paper on a blustery day, it’s plenty enough to make one’s desk appear woefully unmaintained.