uncool

I expect that you should be able to look something up when explicitly told its name. https://en.wikipedia.org/wiki/Law_of_large_numbers "In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed."

As I said earlier: If you don't mean the law of large numbers, then I still can't discern a precise statement you think is false.

Can you make a precise statement that you think is false?

And why, according to you, was there a drop in the intensity of indoctrination of children?

And Ghideon is telling you that you are asking for a proof of something false. As you flip an increasing number of times, the absolute difference between the number of heads and tails will tend to grow, but the ratio of heads will tend to 1/2.

...that's pretty much what Ghideon said.

Do you understand what "absolute difference" means?

That's not an answer to the very specific statement Ghideon made.

He is correct; he is talking about the absolute difference between the number of heads and tails. Only the ratio will approach 1/2.

It sounds like you're asking about the law of large numbers, a theorem known for binary variables since 1713. This is too vague to even mean something. Proof is for specific statements. What is the specific statement that you are asking for proof of? This isn't true, actually. They would find that the ratio of heads would approach 1/2, but that the number of excess heads would diverge from 0.

What "problem"? Probability theory and statistics have been a branch of mathematics since the 1600s, if you start counting with Pascal and Fermat. I have no idea what you are trying to ask here.

...am I the only person to notice which subforum this is in?

There is no sense in repeating the bare assertion, no. If you want to convince us that your assertion is correct, you can write the proof to your assertion - without handwaving. If you want to show that it might be correct, you could demonstrate that wtf's order isn't a counterexample without repeating the assertion as if it were proven fact. But simply repeating it is a waste of your time and ours, yes.

Then the "derivation" is a bare assertion easily shown to be false by the example wtf has provided to you over and over and over again.

We can and have, as wtf keeps pointing out. The order "1/2 <* 1/4 <* 1/8 <* ... <* everything else in the usual order" has 1/2 as a minimum; then S \ {1/2} has minimum 1/4; then S \ {1/2, 1/4} has minimum 1/8, etc. What, precisely, is your derivation?

If by "perfectly derived results", you mean something you believe to be proven, then there is no difference between these two statements. As both wtf and I have said, what you have written does not reach the level of "argument", because it is incoherent. The "point" in all of my questions is to get you to fully explain an argument that you insist on handwaving. It sounds from your post like "Property P" is merely another name for the relation x <* y, and correspondingly, the axiom you seem to claim is that there must be some set S such that for any x and y in S, "x <* y" is not true. If I have that wrong, then please try to write your axiom out explicitly.

I realized that you were trying to refute wtf's implicit claim; it didn't help me figure out how it was supposed to address it.

I have no idea what this is supposed to mean.

So to be clear, it sounds like you are saying P is a property of pairs of elements. Is that correct? Also, are you entirely sure you want to say that xRy if and only if x and y have property P?

It sounds like confused thinking. Here's why: First, you say x and y are related "because" they share a property. Since you are talking about an arbitrary relation R, there is no "because". Either they are related, xRy, or they are not. So how are you defining P? Second, when you say they "share" a property, I infer that you mean that P is a property of a single element. But you keep talking about P as if it were a property of pairs of elements. Third, no matter how you define P, such a set does exist: if S is the empty set, then every universal statement is true on S, trivially.

By whether or not it is true that for every collection-set of sets J_i indexed by I, there is a function f: I -> union of J_i such that for all i, f(i) is an element of J_i. This is a simple true-or-false statement based entirely around set inclusion, which is the basis for set theory. If you want your "axiom" to be used, you will have to be able to specify it to that level (and possibly further). What is your precise true-or-false statement? I really, truly cannot see that there is anything beyond the trivial, essentially that "Different sets have different elements". I am the judge of how things sound to me.

This is beginning to sound like philosophy of math - and, to be blunt, really bad philosophy of math - rather than math itself. I don't see an "axiom" that can be stated based on what you've said, because what you've said doesn't seem coherent enough to evaluate whether it's true or false.

I have no idea what this is supposed to mean.

nm, tried to do something and forum software refused

That only proves that 1/2 is a lower bound for S\{1/2}. Why must it be the greatest lower bound? (Hint: it doesn't; there are many orders where your claim is false) And we've been over why it's wrong a half dozen times. Yes, it is, but it only works well because of the common order on reals. When you lose that order, your intuitions all go wrong, too.