0

I have recently submitted a paper to IEEE Trans. on Information Theory. I got the reviewer comments and one reviewer seemed to me like he/she was obsessive with the notations. For example he was unhappy that I used $\mathbb{R}_{\geq 0}$ instead of $\mathbb{R}_{+}$ for positive real numbers including zero.

In one of his/her comments he asked me to define $$\arg \lim \min$$ which I used in my paper. Before this one, I had used $\lim$ and $\min$ before. I am totally lost about this comments. These are in his list of major comments which led to the rejection of the paper although he/she thought that the paper is a good one in content.

I am now confused about what to do and/or how ro react to this comment. For example saying something like this: "where arg stands for the argument of bla bla bla" doesnt seem to me meaningful because if this is the case I also have to define $\min$ as "where min stand for the minimum of.."

What should be the proper way to react? Is there something that I am missing about this comment?

Seyhmus Güngören
  • 7,848
  • 2
    I'd say that $\mathbb{R}{+}={x|x \in \mathbb{R} \land x >0}$ while $\mathbb{R}{\geq 0}={x|x \in \mathbb{R} \land x\geq 0}$, so I don't get his/her problem with your first notation. – Botond Mar 21 '19 at 11:19
  • @Botond there is another thread here in the forum. I think there is no consensus about it but in my case zero must be included. As long as I read R+is also used mostly for the case where zero is included. So, the editor does not imply that I should not incude zero. – Seyhmus Güngören Mar 21 '19 at 11:21
  • I don't agree. The $+$ notation would be strange in the case of $\mathbb{N}$. – Botond Mar 21 '19 at 12:36
  • @Botond If you aske me I would think it without zero included, as you said. But it seems there is no consensus about it and some people find it really okay to consider it with zero included. Please see this: https://math.stackexchange.com/questions/27968/how-does-one-denote-the-set-of-all-positive-real-numbers – Seyhmus Güngören Mar 21 '19 at 15:34

2 Answers2

2

It might be worth you (cross-)posting this to the Academia StackExchange since this is, in many ways, more about the presentation of your paper than mathematics. However, especially in mathematics, good notation can make ideas much clearer while bad notation can make things harder to understand. Your reviewer may seem to be making a lot of fuss about notation, but they presumably believe that you're making it harder for your readers to follow your argument with your current choice.

Whether that's true or not is not something we can advise on, as we cannot see the paper ourselves.

I personally have no idea what you mean by $\mathrm{arg\ lim\ min}$. I know what the individual terms means, and I know what $\arg\min$ is, but that $\lim$ in the middle is both new and puzzling. To address this, you need to state what you mean by it, not by the individual terms in the phrase. For example,

$$\arg\min_{x \in D} f(x) := \{x \mid f(x)\leq g(y)\ \forall y\in D \}$$ defines $\arg\min$, so if (and I'm guessing here) $\arg\lim\min$ is a limiting version of that, perhaps

$$\arg\lim\min_{x \in D} f(x) := \{x \mid \lim_{n\rightarrow \infty}f_n(x)\leq g(y)\ \forall y\in D \}$$

is what is needed.

postmortes
  • 6,338
  • he will probably ask me what $g$ is. – Seyhmus Güngören Mar 23 '19 at 12:50
  • Well, that's not unreasonable; we should define $g$ there as well, thank you for pointing it out :) Just start with "for $g\in C(D)$ we define..." and you should be good. I know it feels like you're being picked on but (hopefully) the reviewer is just trying to help you reach the point where your readers feel like it's a pleasure, not a chore, to read your writing – postmortes Mar 23 '19 at 12:59
0

  1. Write $[0, \infty)$ for positive real numbers including zero.

  2. $\arg \lim \min$ is not a common notation. Give a definition and the reviewer will be satisfied.

Fred
  • 77,394