Recently, folks have downvoted, closed, and now deleted a question which I feel is a great question.

I suspect that either I will get a fantastic answer here why this is really a terrible question (in advance, thanks for the explanation) or I am hoping that folks will be open to reconsideration for the status of the question.

First, for those who have moderator privileges, here is the now deleted question: Reasoning about products of reals

For a math expert, this question is perhaps so obvious that it is stupid. I would argue that questions are not about what is obvious to the expert but what is helpful to the sincere learner.

The question relates to reasoning about real numbers.

Take 2 sets of real numbers:

  • $x_1, x_2, \dots, x_n$ and $y_1, y_2, \dots, y_m$ such that $\prod\limits_{1 \le i \le n} x_i > \prod\limits_{1 \le j \le m} y_j$.

Let $k$ be any positive real number.

Does it necessarily follow that $\prod\limits_{1 \le i \le n} (x_i+k) > \prod\limits_{1 \le j \le m} (y_j +k)$

The answer is no. This result is so surprising to me that I was excited by the answer!

I understand that professional mathematicians are expected to know this and should do the proper analysis to find the counter example. Not all of us are as gifted in carrying out this analysis. I for one am not (though, I would like to think that my many years on this site has greatly improved my mathematical abilities)

I am not clear why a question and answer that is so important to me was closed and then deleted.

I am fine with the downvote. That would be the expected response to anyone who disagrees with the clarity, quality, or value of a question.

In the case of this question, there was not too much activity so I was not clear why closing was needed. I did not object because I figured that as long as the question was available, the answers were available.

I am writing this to question the forceful deleting the question with the note that the question needs to be revised.

Typically, a question as general as mine would not be accurate. In this case, I think that it is accurate since the question literally relates to the nature of products of reals.

If you have suggestions for improving the title or the question itself I am very open.

If you have explanations for why this is a stupid question that is better deleted, I am very open to that too. I have been active on this site for a very long time and would be very glad to continue to improve in the quality of my questions.

Update: I have updated my mse question to what was intended.

In rereading it, I realize that what was originally asked was unclear and insufficient context had been provided. I have revised it after posting this question.

I have added additional details to provide some context for my thinking.

I leave it to folks here whether the question is worth undeleting or not. Great points were made to why the question is unclear. I appreciate the article pointed out to me by amWhy: How to ask a good question.

I thank everyone for their time in reading this question. I feel that my question has been addressed and am open to leaving the question deleted if that is what folks feel is best for the site. :-)

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    $\begingroup$ You also misrepresent your question, which I repeat in the next comment, in totality: $\endgroup$ – amWhy Dec 27 '20 at 23:13
  • $\begingroup$ "Let: $x_1 > 0, x_2 > 0, \dots, x_n > 0$ be any $n$ reals. $y_1 > 0, y_2 > 0, \dots, y_n > 0$ be any $n$ reals. *with: $$\prod\limits_{i=1}^n x_i > \prod\limits_{j=1}^n y_j$$ Does it now follow that if $k > 0$ is a real that: $$\prod\limits_{i=1}^n\left(x_i + k\right) > \prod\limits_{j=1}^n \left(y_j + k\right)$$" It seems to me that the answer is yes. How does one prove this? $\endgroup$ – amWhy Dec 27 '20 at 23:13
  • $\begingroup$ I repeated the post as it appears now. Perhaps someone "edited the question for you." $\endgroup$ – amWhy Dec 27 '20 at 23:20
  • $\begingroup$ Yes you are correct. I am sorry. My first link was an error. Please see How to ask a good question on math.se $\endgroup$ – amWhy Dec 27 '20 at 23:22
  • $\begingroup$ Using $n$ twice was a mistake. It should have been $m$. I corrected it. $\endgroup$ – Larry Freeman Dec 27 '20 at 23:26
  • $\begingroup$ Interestingly, even with my typo, the answers given do still give counter examples to the corrected version of my question. :-) $\endgroup$ – Larry Freeman Dec 27 '20 at 23:29
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    $\begingroup$ Personally it kind of comes off as a homework/PSQ sort of question. I feel the question might have some merit if you would offer some thoughts as to why you think the equality should hold, or even basic examples you tried where it held. $\endgroup$ – Eevee Trainer Dec 27 '20 at 23:33
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    $\begingroup$ Thanks @EeveeTrainer! That helps. I am 53 so it is not homework. I was working on the Collatz Conjecture and checking my intuition on why the conjecture seems to be true. I was working on an argument related to cycles and was surprised how tough the argument was to make (it turned out by the answer to this question that my intuition was wrong and my argument was invalid). $\endgroup$ – Larry Freeman Dec 27 '20 at 23:37
  • $\begingroup$ @LarryFreeman You are not math fool! Just please play by the rules.And repeatedly updating questions can make commenters and potential answerers feel like they are chasing a moving target. $\endgroup$ – amWhy Dec 27 '20 at 23:54
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    $\begingroup$ Got it! You were refering to the change that I made before. Now I am clear. I always try to play by the rules. I will continue to spend more time establishing context. I will try my best to save this question. I do not make the changes to create a "moving target". I was trying to follow your advice: " If you don't want to improve your post, that's your choice. That's the point. That's your choice to not improve it". I do wish to improve it! That's all I was trying to do. Thanks to you for your help! :-) $\endgroup$ – Larry Freeman Dec 27 '20 at 23:58
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    $\begingroup$ My only complaint about the question is that it's really not beyond anyone's mathematical abilities to do a little experimenting and, with a little bit of thought/luck, come up with simple counterexamples. E.g., $5\times5>1\times24$, but $6\times6<2\times25$. If there's no evidence of a poster doing any experimenting at all, other users will take that as a sign of laziness on the part of OP, and not be inclined favorably toward the question. $\endgroup$ – Gerry Myerson Dec 28 '20 at 8:15
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    $\begingroup$ @gerrymyerson I agree. I will try to do that more in the future before posting a question. I would not have needed to ask the question. The counter example was a big surprise. It shouldn't have been .I see that now. I was looking for confirming examples and trying to prove it rather than looking for counter examples. $\endgroup$ – Larry Freeman Dec 28 '20 at 8:24

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