Notation for set of integers in a range

I would like to identify the minimal value in set of indexed real numbers $$x_1, x_2, \ldots, x_N$$.

Which of these is a good and commonly used notation? Is there a better notation?

• $$\min_{i\in [1..N]}x_i$$
• $$\min_{i\in \{1, 2, \cdots, N\}} x_i$$
• $$\min_{1 \leq i\leq N}x_i$$
• $$\min_{i \in \mathbb N | 1 \leq i\leq N}x_i$$
• $$\min_{i \in \mathbb Z^+ | i\leq N }x_i$$
• why not try $\min \{x_i\}_{i=1}^n$ Commented Dec 28, 2019 at 13:02
• All except the fourth one are valid. I would prefer the third as it is easier to read than the others. Certainly adding the "2" in the second doesn't give any more information than the first. And it is not necessary to say, as in the fifth, that "i" is a positive integer. The fourth is completely wrong as saying "$i\in R$" implies that I might be 1.4 or 2.3, etc. Commented Dec 28, 2019 at 13:03
• @user247327 Thanks, should have been $i \in \mathbb N$ not $\in \mathbb R$. Fixed.
– u17
Commented Dec 28, 2019 at 13:08
• @emonHR Beautiful. Have not seen this notation a lot.
– u17
Commented Dec 28, 2019 at 13:09
• @ste12: The index region should be embraced with curly brackets in the last two examples. Commented Dec 28, 2019 at 18:59

Hint: If we like we can also get rid of using too many indices. For instance:

• Let $$A=\{x_1,\ldots,x_n\}$$ denote a finite set of real numbers. We set $$x_{min}:=\min_{a\in A}A$$.

All first 3 are valid to me, but I never encountered the last two ones.

Looking at the comments, I guess it also depends where you learn maths. Still, i'm using one of those, depending of how much place I have on my paper :

• $$min_{i \in [1,N]} x_i$$
• $$min_{1 \leq i \leq N} x_i$$

This question does not need to remain open. Either of these two seems good. Thanks a lot for your feedback.

• $$\min\{x_i\}^N_{i=1}$$
• $$\min_{1 \leq i\leq N}x_i$$