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In philosophy, a supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. [1] Supertasks are called hypertasks when the number of operations becomes uncountably infinite .
The thought experiment concerns a lamp that is toggled on and off with increasing frequency. Thomson's lamp is a philosophical puzzle based on infinites. It was devised in 1954 by British philosopher James F. Thomson, who used it to analyze the possibility of a supertask, which is the completion of an infinite number of tasks.
This article contains a discussion of paradoxes of set theory. As with most mathematical paradoxes , they generally reveal surprising and counter-intuitive mathematical results, rather than actual logical contradictions within modern axiomatic set theory .
This through-line drives towards a task operating at the scale of the drama as a whole and is called, for that reason, a "supertask" (or "superobjective"). A performance consists of the inner aspects of a role (experiencing) and its outer aspects ("embodiment") that are united in the pursuit of the supertask.
A graph that shows the number of balls in and out of the vase for the first ten iterations of the problem. The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the paradoxical, or at least non-intuitive, nature of infinity.
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Thomson's conditions for the experiment are insufficiently complete, since only instants of time before t≡1 are considered. Benacerraf's essay led to a renewed interest in infinity-related problems, set theory and the foundation of supertask theory.
Indeed, set theory has been formalized as the Zermelo–Fraenkel set theory (ZF). One of the axioms of ZF is the axiom of infinity, that essentially says that the natural numbers form a set. All mathematics has been rewritten in terms of ZF. In particular, line, curves, all sort of spaces are defined as the set of their points.