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?