> The NAFL resolution of these paradoxes is given in Sec. 4 of > <http://arxiv.org/abs/math.LO/0506475> (see Remarks 14-16). Basically > open/semi-open intervals of reals do not exist in the NAFL version of > real analysis -- so the proposition that Achilles is confined to the > interval [0,1) fails and cannot even be stated. Secondly it is not > legal in NAFL to ask *how many* intervals (or reals) are present in the > super-class of intervals ([0,1/2], [1/2,1/4] ....[1,1]), because direct > quantifiication over reals (or intervals of reals), which are infinite > classes/super-classes, is banned. [...]
Correction -- read as "super-class of intervals ([0,1/2], [1/2,3/4], ...[1,1]),"