Supertask
A supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called hypertasks when the number of operations is uncountable. A hypertask that includes one task for each ordinal number is called an ultratask. The term "supertask" was coined by the philosopher James F. Thomson, who devised Thomson's lamp. The term "hypertask" derives from Clark and Read in their paper of that name.
In this literature, a "task" is taken to take a finite amount of time, and at any point in time, at most one task can be in progress. This then shows that hypertasks and ultratasks are impossible, since a finite interval cannot contain an uncountable number of finite intervals. This is because a closed and bounded interval is second-countable.
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