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Yep, it would be like saying 1/1 = 1 Thus 1,000,000/1,000,000 = 1

The percent sign '%' is parts per hundred. ‰ is Parts per thousand and so on. Just simple math :)
 

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The only pure liquid CO2 is what is in a CO2 bottle under about 800 psi pressure. What some people call liquid CO2 is really Excel, and isn't CO2 at all. Excel is very dilute, so it is mostly water.
 

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so if 1ppm = 1 milligram of something per liter of water (mg/l)
This only works for relatively weak solutions if you want any sort of precision. Once you get a concentrated solution, the density of the solution typically changes. It's a pretty good approximation for anything we do though, even up to the ~20,000 ppm used in saltwater tanks. This equivalence only works for aqueous solutions or other solutions with densities very close to that of water (1,000,000 mg/l, specifically.)

More clearly:
Parts per million is found by taking the mass of a particular component of a mixture and divided that value by the total (original) mass of the sample from which it had been removed, then multiplied that value by 1,000,000. It doesn't have to have anything to do with an aqueous solution at all.

Milligrams per liter is determined by finding the mass of a particular solute in one liter of solution, not per liter of water.
 
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