Simplifying assumptions, even those seemingly false, are common in fun math problems. The point is just that, the math. I'm sure the traveling salesman had issues to think about other than the classic math of the problem.
Just for my information, any references to strengthen your last statement?
Atoms, as long as the amount being sequestered in the water or the soil isn't significant. Oxygen is probably a write-off, since there's far more oxygen atoms in the oceans than in the atmosphere, and since O_2 to H_2O is part of animal respiration. Nitrogen, perhaps, might be more constant, but honestly I just don't know enough about the nitrogen cycle to have a good idea.
Ah, but the third most common component of the air is argon, which is deliciously chemically inactive. You could at least compute the probability that you're breathing in some of Caesar's argon.
Simplifying assumptions, even those seemingly false, are common in fun math problems. The point is just that, the math. I'm sure the traveling salesman had issues to think about other than the classic math of the problem.
Of course. And the other thing that's common in fun math problems is that as soon as you're done someone's gonna say "That's great, but..." and point out something you've ignored. It's all part of the game, and I'm just playing along, not being critical.