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Sorry for this rookie question, but we can not treat these ordered pairs as an interval e.g. treat $(a,b)$ as $\{x\in\mathbb{R}\mid a<x<b\}$, under any circumstances, right?

The R
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  • You can if you want, but $ (b, a) $ is distinct from $ (a, b) $ even though they're the same segment, so they don't exactly match up. – Chai T. Rex Oct 20 '18 at 22:30
  • Let me know if the answer is useful, I'm not completely sure about your doubt. – user Oct 20 '18 at 22:42
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    @gimusi Why answer the question if you don't know what it even means? Wouldn't it be better to first ask for clarification, and then, once you have that clarification, answer the question? – Xander Henderson Oct 20 '18 at 22:44
  • @XanderHenderson I understand your observation, the fact is that initially I was completely sure that the main doubt by the asker was what I've answered to. But after reading ChaiT.Rex comment and since the asker has not given any feedback, I would like to receive a confirmation by the asker about that. – user Oct 20 '18 at 22:47
  • @JohnMacT I am confused about what your question is asking. By a "segment", do you mean an interval, i.e. $$(a,b) := { x\in\mathbb{R} : a < x < b }? $$ If so, that is not what the notation $(a,b)$ means in the context of the Cartesian product. In this context, the notation $(a,b)$ indicates an ordered pair, which is a single point in two-dimensional space (and not an interval). – Xander Henderson Oct 20 '18 at 22:48
  • @XanderHenderson Then also your interpretation is like mine! That's good. I hope the asker will give some feedback on that. – user Oct 20 '18 at 22:49
  • @XanderHenderson Yes, that is exactly what I meant, and I am truly grateful to all your answers and comments, I understand now. – The R Oct 20 '18 at 22:53
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    In that case, this question already has an answer here. – Xander Henderson Oct 20 '18 at 22:56
  • @XanderHenderson It seems that my guess was right! Please try to be not so skeptic and relentless with the askers and with who try to help them to clarify their doubts. If my answer was not fitting the asker needing of course I would have deleted that by myself. As I explained before, I was sure of his doubt at the moment I've answered and then I've asked a question to sollicit a confirmation by the asker. Anyway thanks for your suggestion, I understand that you try to act for the benefit of the community but please try also to consider some friendly suggestion from other users! Bye – user Oct 20 '18 at 23:01
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    @gimusi, you miss the point. MSE is not a "guess my question" site. And just because you "read an asker's mind" once in a rare while, while you miss terribly many times elsewhere and need to make multiple edits to correct wrong guesses and your corresponding wrong answers, doesn't mean that the few rare occasions you guess right make guessing a good thing. – amWhy Oct 20 '18 at 23:09
  • The fault is all mine, please don't blame gimusi anymore. – The R Oct 20 '18 at 23:12
  • @amWhy Come on it is completely apparent that your are trying to justify your action by a ridicolous argument, sorry but I've already explained my intention in a very clear way, you can read again if you like. I don't regret to have some doubt sometime, you should try to do the same. Anyway I don't want to continue that discussion, anyone is free here and anyone can judge our behaviours by the facts. Bye – user Oct 20 '18 at 23:13
  • @JohnMacT Never mind for that, unfortunately I'm very used to this kind of behavior. The most important thing is that you have clarified your doubt finally! All others issues are really not so important and go very far from the main goal of this community! Please do not hesitate to ask more for any other clarification. Bye – user Oct 20 '18 at 23:18
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    @JohnMacT The problem here has very little to do with you. You asked a question which was unclear. That is okay---you can still edit it to clarify your question by adding context. When you say a "segment", what does that mean? Is your confusion about the fact that the same notation is used to mean two different things? If so, you might more clearly indicate the contexts in which you have seen that notation. – Xander Henderson Oct 20 '18 at 23:34
  • As amWhy notes, the goal of MSE is to create a repository of questions and answers that will be useful to people in the future, not just you. Adding context to your question and making it more clear will help future readers. – Xander Henderson Oct 20 '18 at 23:34
  • @XanderHendersonI've tried many times to understand that point, could you please me to indicate where I can find the declaration that the (unique?) goal of MSE is to create a repository of questions? I can agree that it could be am important and useful goal but are you sure that it is "The Goal"? Thanks – user Oct 20 '18 at 23:48
  • @XanderHenderson I can also agree with you that the question was not completely clear but why do not ask friendly (according to our CoC) to the asker to improve that and better clarify the point as I was trying to do before your intervention? Do you really think that your way to interact with askers and others users is useful to make things better here? I think that, if you try to change your inclination, your action could be much more effective and useful here. – user Oct 20 '18 at 23:53
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    @gimusi the idea is to ask first for clarification and to answer only then, ie, once the answer was iproved. – quid Oct 20 '18 at 23:56
  • @quid I completely agree with you, that's a good and reasonable way to proceed and I always proceed in that way indeed. As I've explained in that case at the moment I've answered I was sure that the doubt of the asker was the kind of confusion I've answered about. Only after a while and after Chai T. Rex to be completely sure I've asked for a clarification by the asker. Anyway, maybe we have discussed that too much up to now, I don't want to make the issue bigger than that is. Thanks for your suggestion too. Bye – user Oct 21 '18 at 00:02

1 Answers1

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It seems you are confusing

  • the ordered pair which is an element $(a,b)\in\mathbb{R}\times \mathbb{R}$

with

  • the open interval which is a subset $(a,b)\subseteq \mathbb{R}$

beeing $a,b \in \mathbb{R}$, which have the same notation but are two completely different concepts.

user
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  • @user597654 You can read about the dispute in the comments. Thanks a lot for your kind appraciation! Bye – user Oct 21 '18 at 06:17
  • @HennoBrandsma Thanks a lot for your kind editing to correct the bad typo, after discussing a lot about secondary issues we had lost an important detail! Cheers – user Oct 21 '18 at 10:22