Bifurcated supertasks entail the actual infinite division of time (accelerated system of reference) as well as the existence of half-curves of infinite length (supertask system of reference). This paper analyzes both issues from a critique perspective. It also analyzes a conflictive case of hypercomputation performed by means of a bifurcated supertask. The results of these analyzes suggest the convenience of reviewing certain foundational aspects of infinitist theories.

I analyze here Benacerraf's criticism of Thomson arguments on the impossibility of w-supertasks. Although Benacerraf's criticism is well founded, his analysis of Thomson's lamp is incomplete. In fact, it is possible to consider a new line of argument, which Benacerraf only incidentally considered, based on the functioning laws of the lamp. This argument leads to a contradictory result that compromises the formal consistency of the w-ordering involved in all w-supertasks.