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OrphanWilde comments on From the "weird math questions" department... - Less Wrong
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You don't need to do it for all N, just up to the N which the fake oracle is computing. Expected computational time for a randomly chosen N is infinite, but expected computation time for any -given- N is finite.
And only finite time is available- for most N, expected computation time is greater than available time; expected time is constant, and a finite number of N will have computation tine less than any C.