Genady

This does not seem to be a problem. I've asked, and the response was,

It certainly did not. All is clear now, I hope.

That is what that proof was about. If it is not relevant anymore, fine. The other question, has been answered, too. The answer is, yes.

I mean the same that it means in math. I see that.

Its answer is wrong. Try e.g. the triangle 3, 4, 5. Or 3.1, 4.1, 5.

OK. If that is the meaning of his post, then fine. What made me doubt was that he didn't say "wrong answers" but rather "no answer". You always get some answer from ChatGPT, don't you?

Does it have something to do with the OP?

Well, it is not what it was saying. Rather, every natural number is listed, but the set of natural numbers is not.

Literally any shape. Should not touch / cover / contain any points of the grid. IOW, all parts of the shape are between the points of the grid = all points of the grid are outside of the shape. Any shape with a definite area is allowed. The only limitation is that its area is less than unity.

Yes, this list has all natural numbers in it. It does not have a set of natural numbers in it. "Set of natural numbers" and "all natural numbers" are different entities.

I don't know what you mean by the list being "complete." I didn't use this word.

Here it is with a technical modification to fit your new list. We want to show that the set S = {x∈N | x≥1} is not in your list. Let's assume that the set S is in your list. Then there is a row, r, in the list with the set S. The row r has the set R = {x∈N | x=r} Evidently, R ≠ S which contradicts the assumption. Thus, S in not in the list.

Thank you. I didn't know this.

So, the "RCL" in the text you've posted stands for the RCL as defined in this article. Is it correct?

It is your opinion. I disagree, but this is not my point. My point is that, as this example shows, we do not "all know what's wrong..." At least one of us don't know here.

Even if the man is Gaddafi, or Mussolini?

One technical question here. The last paragraph refers to "RCL", but I didn't see it defined above, unlike the "RCF". What does the "RCL" stand for?

I've placed an image in hidden spoiler in my post. It is hidden there, but it is not hidden in the preview on activities list:

Yes, there is. Here is a hint: See where it goes?

Because the sets which appear on the rows in the new list are different from the old list.

That proof has to be modified for the new list. When modified appropriately, it works just fine. I don't see a problem.

Absolutely. I think that has been established some time ago, hasn't it? Why but? It doesn't contradict anything, does it?

The answer is in this statement: This statement means that for every natural number there is a row in the list. That row, by construction, contains that number. Consequently, every natural number is present in some row in the list.