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Imparcticle
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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? ). 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?
Me: As you can see, X, phi (in the form 1.6...) is the only number whose
square is (phi - 1). No other number, as far as I know, has this quality. Apparently, this is supposed to be true for all numbers...
Friend V: No. You can't say "for all numbers".
Me: Ah, because by saying "all" I am quantifying an infinite set of numbers?
Friend V: Yes.
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? ). 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?
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