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Well, you did and you didn't IMO, but bear with me for just a little longer.

Let's say the fraction of A and B in the mixture is FA and FB resp. and that the heat capacities are CA and CB resp. And let's say the temperature of the mixture rises because heat has been added to A which passes some along to B so they're both at the same temperature. Don't you agree that the extra heat will be distributed between B an A in the ratio (FB*CB)/(FA*CA)?

I think you will. O2 and N2 together comprise 99% of the atmosphere and CO2 is 0.0383%. The heat capacity (at 25°C) of O2 and N2 are about 29 J/mol-K and CO2 is about 38 J/mol-K. Consequently the ratio of the heat taken up by the N2+O2 to the CO2 is about (99*29)/(0.0383*38) which is ~1973.

So now, when I said

the N2 and O2 in the atmosphere will take up about 2000 times the amount of heat as the CO2

(and I don't see the practical difference between 1973 and 2000), why did you say I don't understand how this works?

What you said is alright. My point was and still is that the critical absorber is the polar molecules, CO₂ in this case. That is the gas responsible for the heat retention. The other gases are just responsible for taking up the ~6.5W/M² that the CO₂ absorbs at ~330ppmv.

" I don't see the practical difference between 1973 and 2000"

Not sure what you mean here, but there is none. I don't see any significant diff between 1700 and 2060 either.