Notation for set of integers in a range

Question

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?

• $\min_{i\in [1..N]}x_i$
• $\min_{i\in \{1, 2, \cdots, N\}} x_i$
• $\min_{1 \leq i\leq N}x_i$
• $\min_{i \in \mathbb N | 1 \leq i\leq N}x_i$
• $\min_{i \in \mathbb Z^+ | i\leq N }x_i$

Answer 1

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 :

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

Answer 2

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

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

Answer 3

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 $x_{min}:=\min_{a\in A}A$.