If you have any water, you can use it in a closed cycle to recycle CO2 by the Sabatier process and partial combustion of the resulting methane into water and carbon. And you'd need tons of plants in any case to feed everyone.
Robotic surface mining might be possible if asteroids are better used elsewhere. It would rely on a lot of ridiculous materials science, but it would be possible.
Apparently it takes something like 100-300 plants (of varying size) to give a person a healthy diet, according to this website. http://www.wellfedhomestead.com/how-much-should-you-plant-in-your-garden-to-provide-a-years-worth-of-food This is very interesting. So yeah it looks like if you had the gardens to feed 10,000 people (I like Gig's number) then you'd end up with something like:
Let's assume that each leaf produces 5 milliliters of oxygen per hour, each plant has at least 25 leaves, you need 200 plants to feed someone, there are 10,000 people to feed, and a person consumes 50 liters of oxygen per hour.
(200 * 25) * 10,000) / 1000 = 50,000 liters of oxygen per hour
That's enough delicious oxygen to support 1000 people, or a tenth of your total population. That's pretty good. There are too many assumptions for this to be a scholarly estimate but surely the plants would be supporting at least some number of people which is better than nothing.
The main difficulty of robotic surface mining, I would say, is flying the vehicles down to the surface and back up to the colony. I'm still not totally sold on the idea of floating all of your facilities. Foundries, factories, living areas, agriculture, vehicle bays. At least disposing of waste would be as simple as throwing it outside.
I'll also say you'd want more than the bare minimum of plants as well, in case of mishaps where food is lost or plants die. No doubt it'd be a supplement to a different form of oxygen generation, but redundancy is always good and it reduces necessity of outside resources like space or ground mining.
Earlier on in the colonisation process, they could rely on imported dna to help expand their population.
I like that idea. Trading DNA in cold storage for a few thousand adult humans would save loads of money.
It may even be ideal to send DNA in cold storage. It'd probably be more shielded from radiation easier than the actual crew, so it might be in better quality when it gets there, but I'm not sure about that.
But chemical oxygen production could be much more efficient than plants, so why not grow fewer plants that are only for food?
Well, if you can get a closed ecosystem going - or close enough - you've got a lower dependency on outside resources. As oxygen is produced from photosynthesis, it both gets rid of a waste production and produces oxygen while producing said food. You can use plants to recycle faecal matter and other waste products. Having more plants means more food, too, which isn't a bad thing. I don't think anyone is talking about growing plants
just for the oxygen - they'd be food plants.
If you're talking about 10% of the reactors, though, that's the same 10% provided by the necessary crops. I'm saying there's no real need for additional scrubbing plants, because the crops alone will provide enough. And if you're adding more plants, why not make them edible, too? Build up reserves in case of a crop failure.
Edit:
The estimate I've heard as bare minimum for genetic sustainability, so it sounds like you'd be able to keep a small farm-colony stocked with oxygen with plants alone.
That said, I'd consider backup mechanical atmospheric regulation systems to be mandatory.
This is what I was originally responding to, sorry.
It actually reads to me as if Amperzand is missing something in his sentence. Did he mean the 10k figure I mentioned earlier? I mean,
I wouldn't count 10k as a small colony. Regardless, a farm-colony would still suggests the plants are grown for food, just there's enough of them to support a small population on that blimp.