Yesterday I was enlightening a friend of mine concerning the many wonders of Fibonacci numbers and the golden ratio (let this friend be represented as X). As I was speaking with X, I learned that another friend of mine (let him be represented as V) was listening very attentively. Here is our conversation, as it will make things easier for explanation:

Unfortunately, we were unable to continue this conversation on that day. We are scheduled to continue a few days from now.
I actually disagree with V's assertion. This is because of a simple fact: there are certain properties of numbers that have been proved to be true for all numbers (right? :uhh: ). So I could say "all numbers".
But can I say "all of the subsets of an infinite set are such that x is always true for all of the subsets"?
is my usage of the word "all" quantifying my subject? What does the word "all" do in terms of how it quantifies?

Well, what you said is badly phrased, but that's what happens with spoken English, and as alkatran shows incorrect, but it is perfectly possible to make a statement about something being true for an infinite set.

x^2>x for all x in (the infinite set) (1,infinity)

something is true for all elements in some set if the negation, that there is *an* element for which it is false, is false.

Something is true for all the quantified members to which it applies if it is, erm, true for them all.