You need to stick with the convention of using FO2 and ppO2 , it would clarify you’re intent.
Well, fair enough. I surmised based on the comments by others that I was unclear, although it seemed clear to me when I posted it. I'm looking at the NAUI manual (same edition mentioned earlier) now and in chapter 3 it uses the notation FO₂ instead of the greek letter chi (χ). I probably should have remembered that because I did read every page of the manual and practiced all their problems before I took the test.
I sometimes get into arguments with other divers over minutiae. Part of the problem is the notation ingrained in me long before I started diving. I didn't get my first dive cert till I was 33 years old. By then I had a BS in mathematics, an MS in theoretical physical chemistry, and a PhD in experimental physical chemistry and was working as a post-doctoral researcher for the Department of Energy.
For example, Dalton's Law in the textbooks was always presented as
Pᵢ = χᵢ
Pₜ where
Pᵢ is the partial pressure of the iᵗʰ gas in a mixture, χᵢ is the mole fraction of the iᵗʰ gas, and
Pₜ is the total pressure of the mixture. (I have worked with many gas mixtures and used this relationship often in designing experiments.) The dive manuals don't disagree with that, they just don't use the phrase "mole fraction" and "the partial pressure of the iᵗʰ gas" and the symbols they use are slightly different. Same goes for a bunch of other physical relationships. But the notation with which I was already intimately familiar worked for me, so I never bothered to try to memorize the terms and symbols used by NAUI, PADI, etc.
NAUI writes: "The partial pressure of any component gas in a mixture is the fraction of that gas times the total pressure" (The omission of the word "mole" in front of fraction would be a glaring oversight in a physics or chemistry paper and a reviewer would immediately ask about it, because although volumes and amounts are proportional for ideal gases, the mass fractions are very different than the mole fractions used in Dalton's Law. For example, a mixture of N2 and O2 that is 20.9% oxygen by moles would be 23.3% oxygen by mass, assuming molar masses of 28 g/mol for nitrogen and 32 g/mol for oxygen.) You could also argue that diatomics such as O2 and N2 are not very ideal at high pressures so the simple gas laws don't work perfectly (3% error at 200 bar, 10% error at 300 bar), but that's getting into the weeds.
I guess that's all stuck in my head long before I started diving. I will say that all of the instructors I have had were tolerant of my over-analyses. In fact, a couple of them have expressed admiration for it. One even invited me over for dinner with him and his wife, also a dive instructor, and we discussed diving physics at length. In his day job he was an engineer, and I know that they sometimes use different notation and terminology than scientists, so he was probably already used to translating that sort of thing in his head.
I think I also now understand the question about the relative importance of DCS vs oxygen concerns. I only mentioned using the higher number for the profile (and in my head profile refers to depth), and I didn't post anything about run time or TNT, so maybe it seemed that I was thinking of oxygen more than nitrogen. But I'd say that on an average dive I probably think more about nitrogen. Sometimes I even hang far longer than three minutes at 15 feet on those tropical recreational dives, if the dive leader will put up with it. Especially if the water is clear and there are turtles and fishes and dolphins to look at.