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I just posted a question. I took my time to write it. I thought it was a good question. Less than an hour later, and the question has been downvoted 4 times. I thought "okay, I clearly said something wrong, so I'll just delete the question, carefully reread this paper and ask it again." But then, someone had already posted an answer.

Not terrible, but not ideal.

What bothers me is that it took only a very short time for the question to be downvoted, and I'm still not sure what was wrong with it in the first place.

I wasn't provided much feedback on how the question could be made better (in terms of content, at least, the now edited-out all-caps remark was admittedly a bad idea on my part), and I don't see how I could have anticipated the response I recieved unless I had possessed sufficient knowledge to answer the question in the first place.

I understand that it is important to maintain the quality of questions on SE - but when I post a question, it's usually because I lack expertise and have failed to come up with an answer on my own.

In any case, how should I have asked the question? How can I avoid having my questions downvoted immediately? And how can I encourage users to tell me why my question was flawed rather than just downvote and/or vote to close without saying anything?

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    $\begingroup$ Specifically in this case, I think mistake number one was to call those logical fallacies of the countability of the continuum "proofs" and then claim in a parenthetical remark that their status is "indeterminate". That is purposefully inflammatory. If you later edit to remark that the continuum is uncountable, then you already accept that those "proofs" are fallacious and not "indeterminate". Why use that language, then? $\endgroup$
    – Asaf Karagila Mod
    Commented Apr 25, 2019 at 19:35
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    $\begingroup$ @AsafKaragila Because any attempt to verify said proof in the language of the theory used to write it would result in "cannot be proven true or false". It is a 'proof' in the sense that it is a formal argument demonstrating the truth of some premise - in this case to the extent that the statement "'$\mathbb{R}$ is countable' is not false" is true. The problem is that the class of objects to which that premise applies does not exist. $\endgroup$
    – R. Burton
    Commented Apr 25, 2019 at 19:44
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    $\begingroup$ @AsafKaragila The point of the question wasn't even to consider the countability of the real numbers, I even said as much - it was to restrict the notion of 'class' in a way that would prevent such a 'proof' from even existing. The problem was that 'class' was under-specified. $\endgroup$
    – R. Burton
    Commented Apr 25, 2019 at 19:48
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    $\begingroup$ A proof is a sequence of logical statements which are either axioms or derived from previously appearing statements using inference rules. And the statement proved is the last statement in the sequence. Proofs are not "indeterminate" nor they are "true" or "false. The statement is proved or it is not proved. You could claim that you are unable to verify for yourself whether or not something is a proof. But it does not make it a proof nor takes that status away from it. The point is that if you know that $\Bbb R$ is uncountable, any claim that it is countable is provably false. Period. $\endgroup$
    – Asaf Karagila Mod
    Commented Apr 25, 2019 at 19:59
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    $\begingroup$ (And I understand this is not the focal point of your question. But you can appreciate why it severely detracts from any other point you are trying to make or have clarified, right?) $\endgroup$
    – Asaf Karagila Mod
    Commented Apr 25, 2019 at 19:59

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Disclaimer: I hadn't seen your question before following the link in this meta question. I'm basing this answer on the first revision of the question.

  1. The title is the title, not the first sentence of the body. The question appeared to start (and still does) with a parenthentical sentence which is lacking context, and that's a bad first impression.

  2. This is followed almost immediately by an example:

    For example, the set of even numbers is the class of integers divisible by $2$.

    This is not phrased with the caution I would expect from someone who understands the distinction between sets and classes.

  3. What is important is that the proof relied heavily on exploiting a loophole in the definitions of 'function' and 'class' in a way that I felt should be disallowed ... the premise is this:

    If $f$ is a mapping ...

    Again, this looks like sloppy use of language (or use of a non-standard definition of function without including it for context).

  4. If $f$ is a mapping from an infinite class $X$ to an infinite class $Y$, such that for all elements $x\in X$ and $y\in Y$ no computation can be performed to determine $f(x)=y$, then it is impossible to prove the statement "$f$ is a bijection from $X$ to $Y$" false.

    That's a false premise: it seems to assume that all proofs are constructive. I could define $f$ in such a way that its codomain is a single element which can't be computed. Or I could take your function $f$ and lift it to a function $f' : X \to \mathbb{N} \times Y$ as $f'(x) = (1, f(x))$.

I haven't even got to the question yet, and already I have a strong impression that (a) it's going to be unanswerable because it's built on invalid foundations; (b) insufficient effort has been given to communicating clearly.

When I get to what I take to be the actual question:

If we have an infinite class $Q$ whose elements are truly arbitrary, then there is no way to determine $q\in Q$ for all $q$, right?

I find that it's unanswerable for a different reason. What does truly arbitrary mean? (This has been improved slightly in the current question, although I still don't think the definition given is precise). What is the scope of that "all"?

To be honest, I'm surprised that the question wasn't closed as "Unclear what you're asking".

So on the flip side, how to do better next time.

Write the title last. Not only does that prevent you from treating it as context for the opening paragraph, but it means that when you write it you're at the end of the process of thinking about the best way to express your question succinctly, so the conditions are more favourable for a good title.

Use language precisely. That's more important in some subfields than others, but naïve set theory and logic do not handle sloppy language well. Pay particular attention to quantifier scope, and rewrite sentences or even use $\forall x: (Y)$ notation if necessary.

Define any terms which might be ambiguous. (And even when they're not ambiguous, sometimes writing out the definition of the key term is enough for the "Aha!" moment).

Get to the point. If the background is useful but long, it might be best to put the question first and then fill in the background.

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    $\begingroup$ "Write the title last" and the paragraph explaining the rationale of doing so are worth their length in gold. $\endgroup$
    – Asaf Karagila Mod
    Commented Apr 25, 2019 at 19:55
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    $\begingroup$ @Asaf How much is a meter of gold worth? $\endgroup$
    – Tobias Kildetoft
    Commented Apr 26, 2019 at 5:14
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    $\begingroup$ @Tobias: Roughly 50 meters of silver. $\endgroup$
    – Asaf Karagila Mod
    Commented Apr 26, 2019 at 10:30

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