Can you talk about (the rest of the) field axioms when the operations are not closed?

Ok I'll admit it was bad at first. Unfortunately downvotes sometimes show not really show how bad a question is but simply that it was bad and popular (like in an infamous kinda way instead of famous kinda way obviously...I guess).

Anyway I've edited to just 1 question now. Also I took off the things...

  1. about the field axioms (deleted altogether)

  2. the details for the stochastic calculus thing (I asked this on Quant SE but it was closed there too.)

  3. and the distinguishing (moved to another question w/c got 4 upvotes and 0 downvotes initially).

I also explained why I believe it's justified to cross post to Mathematics Education SE, although I was kinda cheating in asking the same question but merely hoping for a different answer. It was closed there too.

Question 1: Any other suggestions?

Question 2: I also wanted to know what happens when you get 5 close votes but not for all the same reason?

  • $\begingroup$ @JitendraSingh oh why thank you! binary just means closed like if the operation $f:S^2 \to \mathbb R^n$ really is able to restrict to $S$ because $image(f) \subseteq S$ $\endgroup$
    – BCLC
    Commented Sep 22, 2021 at 10:28
  • 3
    $\begingroup$ I would say "binary operation" means an operation with two arguments. So $x+y$ is a binary operation, but $-x$ is a unary operation. $\endgroup$
    – GEdgar
    Commented Sep 22, 2021 at 10:39
  • $\begingroup$ @GEdgar it's about the range not the domain. the domain is indeed 2 arguments. but the range is not necessarily $S$ $\endgroup$
    – BCLC
    Commented Sep 22, 2021 at 10:44
  • $\begingroup$ Are you asking about the "Can you talk...." question, or about the "generalising-or-intuition...." question, BCLC? $\endgroup$ Commented Sep 22, 2021 at 11:20
  • 4
    $\begingroup$ If you're asking about "Can you talk....", I think the way to improve it is to burn it up completely, start over again, leave out all the superfluous nonsense, just get to the point, ask the question, end of story. $\endgroup$ Commented Sep 22, 2021 at 11:32
  • 13
    $\begingroup$ My opinion is that your posts (not just this one) are characteristically long and not to-the-point. Even after reading the question (quickly, I’ll admit) I have no idea what you are asking. You still mention field axioms in the title. You still mention stochastic calculus. Even in this meta post, you said ‘popular (like in an infamous kinda way instead of famous kinda way obviously...I guess)’ this is far too much. You do not need to be so conversational. I don’t need to know how you figured out that ‘infamous’ is the correct word. The entire part I quoted can be replaced with the one word. $\endgroup$ Commented Sep 22, 2021 at 12:13
  • $\begingroup$ @CalvinKhor i wasn't sure infamous was the right word. but thanks! $\endgroup$
    – BCLC
    Commented Sep 22, 2021 at 20:00
  • $\begingroup$ You’re welcome @BCLC; sorry it’s a little blunt and terse (also regarding your edit, your interpretation of the meta question votes is not always applicable; I didn’t vote on the question but I voted up on the answer below) $\endgroup$ Commented Sep 22, 2021 at 22:50

1 Answer 1


Is there anything to improve in this post?

Yes. A lot.

  • Remove your commentary about the downvotes.
  • Remove your commentary about the close votes.
  • Move your comment about the cross-posting to a footnote at the bottom of your post.
  • Remove your pre-emptive response to people judging your post.
  • State the homework question in full. There is no benefit—and arguably a lot of detriment—to the clarity of your post in saying

    Let $S$ be the subset of $\mathbb{R}^n$ s.t. (details details).

  • It is irrelevant whether or not the exercise is phrased in the way it is in order to trick the student. Only your instructor can answer about their intention (or lack thereof) to trick you through this exercise. So, remove your commentary about how this appears to be a trick question.
  • Remove irrelevant links such as:
    • The link to your old question on optimization, linked behind the word "response". It has no relevance to this question.
    • The link to "Red Truth | 07th Expansion Wiki | Fandom" behind the word "loophole". Whatever the point is that you're trying to convey by this link, you can certainly do it in a more transparent fashion. But my strong suspicion is that there trying to weave this into your post will not benefit it in any way, and your post will only improve by removing the link.
    • The links to your related questions on idempotent matrices and on a question in your stochastic calculus exam. They are only related in the sense that in those questions you seem to have encountered some ambiguity in the phrasing of some problems. Reading those links does not help to clarify your current question. It certainly does not contribute relevant context to your main question(s).
    • The link to User Tommi's answer to your question on Academia SE about inadmissible theorems in research. It has no bearing on this post, and I am almost tempted to question whether you might be shoehorning these links simply to promote your other questions.
  • Rewrite your primary question. There is no point in asking whether something is fair or not. You need to have a discussion with your instructor about any perceived fairness or unfairness in your assigned exercises.
  • Remove the reference to the problem about a continuous function attaining each of its values twice. Again, it has no relevance to your primary question, and only serves to distract.
  • Remove your associations with chess puzzles and locked room mysteries. They don't help to clarify your primary question, and you're sending people off on more wild goose chases with even more links.
  • You've got an answer to your related question about how and why the operation $+$ on $\mathbb{R}^n$ is not distinguished in notation from the operation $+$ on $\mathbb{R}$. Clearly spell out in this post what confused you about the notation and why that is not the main confusion after having received an answer to your other question. This will allow any answerers to not unnecessarily repeat what was already clarified in the other post, and give focused answers to your current problem. On the other hand, if that post is not relevant in clarifying your primary question here, then remove it completely.

If you can do all this, then your post should read something like this:

In my course <MA 000>, my instructor posed the following exercise:

Quote the exercise in full.

Here is the definition of a field as taught in class:

Quote the definition you are using in full.

Now, I notice that the given operations $+$ and $\times$ on $S \times S$ are not binary operations on $S$ because as per the definition of binary operation that we are using in class

Quote the definition you are using in full.

the range should be contained in $S$ in order to call them binary operations on $S$, but that is not the case here. So, my question is about how I should interpret the question of whether the operators satisfy any of the axioms of a field. Since they are not binary operations, do I immediately conclude that they do not satisfy any of the axioms? Or, would it be correct to ignore the fact that these are not binary operations and just verify whether (say) commutativity holds, etc.?

Note: I asked my instructor about this and they responded as follows:

Quote the instructor's response.

  • 19
    $\begingroup$ +1 for the detailed answer. That really needs some effort to think and write. I hope this leads to a genuine improvement of the question under discussion. $\endgroup$
    – Paramanand Singh Mod
    Commented Sep 22, 2021 at 13:49

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