# "Delicacy" vs. "subtlety" vs. "fragility"

I would like to use a word meaning that something (not food) is delicate.

More precisely, assume that there is one (mathematical) hypothesis R-H; it is not known if it is true or not.

We know that the cardinality of a set M of numbers is infinite if and only if hypothesis R-H is true.

I know it is possible to prove that some supersets of the set M is infinite, that is somehow in favor of hypothesis R-H.

Now if I want to say something about that hypothesis R-H, which one of the following is better? Or is there a better alternative still?

1. We show the delicacy of the R-H in terms of some supersets of M.
2. We show the fragility of the R-H with respect to the terms of some supersets of M.
3. We show the subtlety of the R-H in terms of some supersets of M.
• There seems no connection to me between knowing that sets S1, S2... are infinite and that a subset of all the S's is infinite if and only if R-H is true. You can always form any number of infinite supersets from any given set by union. Feb 9 '14 at 23:10
• If this is a technical mathematical question, you can name it anything you want as long as you give a definition. If this is about the proof strategy situation, so that you are using the word metaphorically, 'subtle' is way too metaphorical and judgmental. 'Delicacy' sounds too much like food, but 'delicate' might work (where the proof could easily fall apart), and 'fragile' or 'fragility' will work but are maybe too strong (will really fall apart. This is all composition judgment; see if other mathematicians use words like these in proof strategies by a google search. Feb 10 '14 at 18:38