Persuasive enough, mathematically. Practically, though, people wouldn't allow the definition to recurse like that. Consider a hypothetical person filling in d

Persuasive enough, mathematically. Practically, though, people wouldn't allow the definition to recurse like that. Consider a hypothetical person filling in descriptions for all the interesting numbers. "Smallest prime", "Smallest odd prime", "Smallest square" . . . He would get to the smallest uninteresting number and write, "Smallest uninteresting number." Then when he got to the next one, he'd start to write that, realize he already had one, and ponder for a bit. The divergence occurs here. If he was a mathematician, he would shout, "Aha! There are no uninteresting numbers!" If particularly diligent, he would go on to write "Was the smallest uninteresting number until that made it interesting" on all the other numbers. If he was a normal person, he'd criticize the definition. Yes, he does think the smallest uninteresting number is interesting, but he doesn't think the next one is. So the technical definition shouldn't be recursive, and that keeps the initial annotation from being so self-defeating. He'd then go back and write, "Smallest number which would otherwise be uninteresting" on the first one, and leave the rest alone. I side with the normal person. A definition which allows so many numbers with the same description to be considered "interesting" doesn't actually correspond with what I think interesting means. I think it is reasonable to require that the definition of interesting be stable regardless of what order you evaluate the integers in, so a definition that allows for this sort of nonsense should be modified until it doesn't.