@Prithubiswas: By the way, since you saw my messages in the other room on the cheating attempt (here and here), if you agree with me could you also flag it for closure? Although you don't have much rep, your flag will actually count towards the close-review.

@user21820HATESSMOKING-HATS I agree that the question should be closed because there was a cheating attempt from double knot. However , I don't know which category I should flag (This is my first time flagging).

Mod intervention?

As you mentioned in miscellaneous, Double Knot is suspicious

@Prithubiswas Click Flag > Needs Improvement > Community-specific reason > Lack context (or something like that).

@Prithubiswas Best not to mention usernames too often.

@user21820HATESSMOKING-HATS Oh ok my bad.

@Prithubiswas No not a problem; it's just to avoid honey attracting the flies.

=P

By the way, did you manage to understand roughly Godel's incompleteness theorem from my post?

Since you understood the halting problem unsolvability, and you know a bit of programming, and you know a deductive system for FOL, you almost know enough to understand that part at least.

Did you succeed in flagging? It's not user-friendly that the close options are hidden behind "needs improvement", as some questions simply ought to be closed without improvement. But that's what it is. I actually had to go to another site to see what you would see, because it's a different menu once you reach 3000 rep.

@user21820HATESSMOKING-HATS Yep I succeeded. I have mixed feelings because I never even downvoted anything :P

Anyway for some reason the privileges on Chess SE have lower thresholds, so if you participate there you can easily reach the top hahaha..

I didn't realize it all the time I was there until I reached 2k rep and noticed I could cast delete-votes (which needs 20k rep on most sites).

@user21820HATESSMOKING-HATS I am currently trying to understand it.

@Prithubiswas Great. If you are uncertain about any point, just ask straightaway. To make that post fit into a single Math SE answer, it assumes some background knowledge, and the later parts assume rapidly increasing amounts.

@user21820HATESSMOKING-HATS

Can you clarify a bit about the "obj" type in your post?

What is exactly this "obj" type and what is "universe"?

Can the "obj" type have only 3 things or 7 things or be empty?

@Prithubiswas It's just there so that you can quantify over literally everything. If you only care about ℕ and subsets of ℕ and subsets of other already existing sets, then as you might have noticed you didn't need obj at all.

@Prithubiswas The universe rule says that every meaningful expression you write down in any context is a member of obj. This rule captures the notion that obj is the type of literally all objects.

For instance, we can prove ∀x∈ℕ ( x∈obj ), as well as ∀x∈set ( x∈obj ).

Note that my system didn't assert that every member of ℕ is a set. If ZFC is consistent, you won't be able to prove ∀x∈ℕ ( x∈set ). Intuitively the system is agnostic about what the members of ℕ are; all it says is that ⟨ℕ,0,1,+,·,<⟩ satisfy those axioms of PA, and the ST part adds that ℕ is a set, otherwise the set theory part becomes quite useless.

More generally, the system does not assert that every member of a set is also a set. Such set theories are said to permit urelements. This distinguishes my system from pure ZFC, but there is no essential difference in what both systems can do, and in my opinion it is better pedagogically to have a mental separation between sets and objects.

If a question asks "What percentage is a half?" Is the answer 50%, or 50? Or is the question ambiguous? Is the question gibberish?