I would like to specify the set $\{0, 1, 2, \dots\}$, i.e., non-negative integers in an engineering conference paper. Which symbol is more preferable?
- $\mathbb{N}_0$
- $\mathbb{N}\cup\{0\}$
- $\mathbb{Z}_{\ge 0}$
- $\mathbb{Z}_{+}$
I would like to specify the set $\{0, 1, 2, \dots\}$, i.e., non-negative integers in an engineering conference paper. Which symbol is more preferable?
According to Wikipedia, unambiguous notations for the set of non-negative integers include $$ \mathbb{N}^0 = \mathbb{N}_0 = \{ 0, 1, 2, \ldots \}, $$ while the set of positive integers may be denoted unambiguously by $$ \mathbb{N}^* = \mathbb{N}^+ = \mathbb{N}_1 = \mathbb{N}_{>0}= \{ 1, 2, \ldots \}. $$
Based on this similar post, the following seems to be preferred:
$\mathbb{Z}_{\geq 0}$
Wolfram Mathworld has $\mathbb{Z}^*$.
The set of numbers $\{0, 1, 2, \dots\}$ is well-known as the set of whole numbers $\mathbb{W}$.
I personally always use $\Bbb N_0$ because what you are really describing is just the natural numbers plus the element $\{0\}$.