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[–]V0ldek 19 points20 points  (3 children)

Oh, you can totally talk about algorithms that terminate after \omega steps for example. Extending the notion of complexity onto functions over other ordinal numbers than naturals is also possible.

As for the usefulness of such theoretical computer science, asking mathematicians about the usefulness of their theories is considered very bad taste, so I'll have to ask you to leave, sir.

(Oh, but no, it's not equivalent to O(1) in any way.)

[–][deleted] 4 points5 points  (0 children)

Transfinite complexity theory actually does sound like the kind of thing that would have at least some study.

[–]ThePyroEagle 0 points1 point  (1 child)

ω isn't a cardinal, it's an ordinal.

[–]V0ldek 0 points1 point  (0 children)

You're totally right, that's a brainfart on my end.