Ok I see I emphasize the word QUANTITY and everyone keeps harping on about the ratio. Of course the ratio is the same. There is still 80/20 Nitrogen vs oxygen. But there's less O2 and less Nitrogen. You may end up climbing up to the top of Everest and you may end up getting 2 02 molecules and 8 Nitrogen molecules in each gasp of air (not actual numbers, I'm just trying to illustrate that the ratio stays the same).
And Eugene, the diving example of taking air at a location and compressing it and then taking it to a different location is invalid. We up here joke about bottling sea level air and taking it up to altitude. Although it's a joke, that's what you are taking about. Bottling oxygen rich air.
The air at the second location is LESS DENSE. IT has less of of everything. Why do you think there's less drag at altitude. See how your car accelerates from 250 to 300km/h at altitude? Try that in the thick muggy coastal air and the car takes longer (with more power) to reach 300. The car is much more slippery at at altitude due to less resistance. So is there less air there for a given volume? No, the volume is the same. Thes is just less "stuff" in the air and everything is spread further apart.
I have practical examples where you crank the presssure a couple psi to compensate (on my turbo cars), and you still make nowhere near the power you dyno at sea-level. And the car spools so much quicker at the coast and peaks so much later (with big turbos that are not outside their efficiency islands).