A supertask refers to an infinite amount of actions in a finite amount of time.

This is analogous to other "super"-things, like supersolids which are solids with a finite volume, but an infinite surface area (like Gabriel's horn, or other ones that don't have to be unbounded in linear size).

How To Count Past Infinity

Another mathematical object defined as a limit are space-filling curves, described in this video by 3Blue1Brown, that also explains the usefulness of infinite results in a finite world. Basically, infinite results are always described as a limit of a sequence of finite results. And these finite results themselves are useful. The concept of infinity is still useful because it allows to understand and summarize these finite results in simple ways.

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perhaps only those concepts to do with infinity which can be expressed as a a limit of finite concepts are useful

(idea)Yeah, a single limit infinite corresponds to {thing is arbitrarily large}, an ordered sequence of limits corresponds to things like {thing2 is arbitrarily larger than thing 1} etc! See big Hmm at Borel-Cantelli lemmas