# Tuple notation for non-negative integers

I have three variables $$x_1, x_2, x_3$$ that can only be non-negative integers, i.e., $$x_1 \in \mathbb{N}_0$$, $$x_2 \in \mathbb{N}_0$$, and $$x_3 \in \mathbb{N}_0$$. Is it correct to write this in a tuple like $$(x_1,x_2,x_3) \in \mathbb{N}_0^3$$? If not, what is the correct way?

• that is correct Mar 30 at 3:15
• Yes, or $(\Bbb N_0)^3$ for more clarity. Mar 30 at 3:26
• Another option for writing it is to enclose the $\mathbb{N}_0$ in braces, giving you ${\mathbb{N}_0}^3$. I'm not sure I actually like that, though. Mar 30 at 18:28
• @TannerSwett - Oh, you mean add braces in the underlying LaTeX, so that the superscript isn't directly over the subscript! I kept thinking "I don't see any braces" and wondering if my rendering was broken. Mar 31 at 17:45
• @JonathanZsupportsMonicaC Yup, sorry for my ambiguous writing! Mar 31 at 23:16

$$x_1, x_2, x_3 \in \mathbb N_0$$
Yes, this is correct. You could also write $$(x_1,x_2,x_3)\in\mathbb{N}_0 \times \mathbb{N}_0 \times \mathbb{N}_0.$$
An alternative that avoids duplication is $$\text{x_i\in \mathbb{N}_0 for i\in \{1,2,3\}}.$$