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General chemistry question: CO2 & O2

Hi, All.

On another forum, I got myself into a discussion that might end with my 
having to eat crow. Well, to keep it brief, can anybody explain to me why 
[CO2] and [O2] would be completely independent of one another in water? I 
argued that you can only have a certain amount of dissolved gases in 
solution under atmospheric pressure (constant P, V, and T), and that 
elevating the concentration of CO2 in water WILL displace O2 to some 
degree. The other person said that one has nothing to do with the other. I 
seem to have heard the same argument in the past, with his explanation 
being correct, but my intuition says that if you kept pumping a certain gas 
into water, you're not going to maintain (in solution) the same amount of 
"other" gases that are not being pumped in... It just doesn't make sense to 
me. So I need to have it explained to me why you CAN'T "displace" O2 no 
matter what. I mean, if you keep pumping pure nitrogen gas into water at a 
significant rate, MY MIND pictures all other gases being "pushed out" of 
solution. I know the principle of partial pressures only applies to gases, 
but I feel like there was a similar principle for gases dissolved in liquid.

My husband just put my chemistry books into the garage and I'm too lazy to 
get them out. If somebody could give me a formula and simple explanation, 
I'd really appreciate it. Thanks. I hate eating crow...