Regarding Closure of my thread

[SSequence]

There are few things that I would like to mention regarding the closure of my thread. It isn't unusual for some thread to be closed by a mod without an ordinary user getting the chance to respond. And of course, one wouldn't want to make a separate thread about every such topic. I did want to clarify one aspect here.

Here is the link:
https://www.physicsforums.com/threads/an-argument-involving-well-orders.998716

This thread isn't necessarily about asking the thread to be re-opened etc. There is one thing I did want to address (and hence the main reason for making this thread). My question was NOT: "Why I got the downvote?" Of course such a question would be vague (and subjective). Not useful to ask that kind of question (on another site).

In hindsight, maybe I shouldn't have made any mention of downvote etc. at all. Since a mention does tend to give the impression that the question isn't about correctness/incorrectness of actual question or post, but something else.

My question was: "What is wrong (if something) with the reasoning I wrote?"

==================================================

Few specific (miscellaneous) points. Idk whether I should mention these, since the primary reason for making the thread was the first half. But anyway, since I already made this thread, few brief points.

@fresh_42

I think you use a lot of concepts without actually knowing how. E.g. the problem with the definition of A+B where you used the projections 'first' and 'last', but you do not have a direct product, so what is it? An example with numbers cannot be generalized. You can always use the lexicographic ordering on the pairs of A and B, however, you used a sort of addition.

I was simply considering A and B as subset of real numbers. Every subset of real numbers defines a linear-order (under the usual comparison relation for real numbers).

I don't remember much group theory (if any at all) without referring or looking-up [even then I only learned the very basics]. So I don't know what to say about what you wrote.

I did not get the impression that you have this knowledge on set theory and logic, i.e. a professional level...

That's correct indeed. I have never said otherwise.

Nevertheless, the idea of what I was trying to do was simple. Build an increasing sequence of ordinals and use that to create an infinite descent in set B. The ill-definedness of function first was indeed a problem. As I understood, it was correctly fixed by the definitions I re-wrote [but it would be nice to have that re-affirmed].

 

[Vanadium 50]

It sounds like you got a downvote at another site, came here to complain about it, got the thread closed, and came here to complain about that.

You asked what was wrong, got an answer, didn't like it, and argued about it and continue to argue about it in this thread.

Maybe you should let it go.

 

[SSequence]

It sounds like you got a downvotye at another site, came here to complain about it, got the thread closed, and came here to complain about that.

Yes, I do agree that it did sound like complaining. I have a tendency to get a bit verbose at times (trying to explain everything and all that). However, it wasn't complaining. Ofc I was a little bit upset. But the question was fundamentally about correctness/incorrectness.

That's why I wrote:

In hindsight, maybe I shouldn't have made any mention of downvote etc. at all. Since a mention does tend to give the impression that the question isn't about correctness/incorrectness of actual question or post, but something else.

But I think it would be agreed (or perhaps even recommended) that if one sees a question somewhere else and wants to post it here (with or without a proposed solution), then one would want to link to the source (or wherever the question was first seen).

You asked what was wrong, got an answer, didn't like it, and argued about it and continue to argue about it in this thread.

Perhaps it seems like that, but it isn't about liking or disliking an answer given. For example, see post#9 in the thread. A clear mistake/deficiency was correctly pointed out by Office_Shredder in post#7 and I immediately acknowledged [there isn't any point not to acknowledge a mistake if one happens to recognize/understand it] it in the next post describing how to fix it.

What I asked in post#9 was simply whether that fix works or not (just to be sure). If you ask me, I think it (quite) likely does [also there is no issue with acknowledging if it doesn't, if the reason given precisely points out why]. Ofc it would be nice to have that re-affirmed, but nevermind.

At any rate, whether correct or not, it was a basic kind of argument. So probably spending too much time on it might not be helpful.

Maybe you should let it go.

Yeah, probably that would be for good. Peace :p.

 

[SSequence]

It sounds like you got a downvote at another site, came here to complain about it, got the thread closed, and came here to complain about that.

I do have one small question about posting in general. What do you (or mods) suggest would be a good way to post (so that it doesn't look like complaining) from some other source/link [1]. One template might be:
---- "Thread Title"
---- Link to original question or source
---- Post the question/answer to be discussed (for accuracy or for discussion)

So no discussion about anything that isn't related to specific topic. So if I posted a thread in that template would it be OK or is it the case that there is some kind of (specific) policy against cross-posting that I am not aware of?[1] Since apart from this site, I only post at MSE/MO, that's likely to be the link for me (in case of cross-posting)

 

[mfb]

There is no need for a specific template, that doesn't matter.
Discuss the topic, not the discussion.

 

[SSequence]

There is no need for a specific template, that doesn't matter.
Discuss the topic, not the discussion.

Are you talking about the specific topic at hand. For that, for example, you can see my replies to the quotes in OP. Other than that probably what I posted in post#3 is relevant:

Perhaps it seems like that, but it isn't about liking or disliking an answer given. For example, see post#9 in the thread. A clear mistake/deficiency was correctly pointed out by Office_Shredder in post#7 and I immediately acknowledged [there isn't any point not to acknowledge a mistake if one happens to recognize/understand it] it in the next post describing how to fix it.

What I asked in post#9 was simply whether that fix works or not (just to be sure). If you ask me, I think it (quite) likely does [also there is no issue with acknowledging if it doesn't, if the reason given precisely points out why]. Ofc it would be nice to have that re-affirmed, but nevermind.

One other point. The objection raised very early in the thread, while reasonable, but doesn't affect whatever I wrote (at all). I tried to explain that in the next 2 or 3 posts.

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Also, moderation is a thankless job. Besides that on some more advanced topics [like the tricky topic of definability in sets etc.], I definitely have had lot of imprecision in my writing before (and probably a lot of mistakes too). But nevertheless, a lot of these were honest mistakes or short-comings [partly though, these are part of learning]. So a post with lot of symbols can reasonably look like throwing around fancy terms mindlessly.

==========================================

Though the specific topic in question was/is relatively basic. On the very least, the concepts involved are not difficult to understand intuitively [sometimes the "formal"/"full" set-theoretic justifications of even the basic concepts indeed require a more detailed apparatus ... and I am not aware of some of it].

For example, just getting to specifics, I can kind of explain with a couple of examples (if I am not messing up the examples). Consider the following sets:
$A=\{1/n: n \in \mathbb{N}^+\}$
$B=\{1+n: n \in \mathbb{N}^+\}=\{2,3,4,5,6,...\}$
$C=\{0.5,0.75,0.75+1/8, ...\}$

Now let's consider various sets (the ordering relation below and in the question is usual comparison relation for real numbers):
$A$ is not well-ordered
$B$ is well-ordered and has order-type $\omega$
$C$ is well-ordered and has order-type $\omega$
$B \cup C$ is well-ordered and has order-type $\omega \cdot 2$
etc.

So what was the original question? That was that given two well-ordered subsets of $\mathbb{R}$ (under comparison of real numbers) $A,B$ if we write $A+B$ to denote $\{a+b \,|\,a\in A \wedge b\in B\}$ ($+$ denotes the usual real number addition) then can we show that $A+B$ is also well-ordered? The answer seems to be yes. So the topic I made was for discussing a suggested solution for that question.

Hopefully that clarifies things a bit further.

 

[mfb]

Now you are discussing the discussion of the discussion.

I think everything relevant has been said in the original thread and I don't see a point in continuing either that discussion or this thread.