Index of notation/N

Expression	Status	Meanings	See also
$\mathbb{N}$	current	The natural number (or naturals), either $\mathbb{N}:=\{0,1,\ldots,n,\ldots\}$ or $\mathbb{N}:=\{1,2,\ldots,n,\ldots\}$. In contexts where starting from one actually matters $\mathbb{N}_+$ is used, usually it is clear from the context, $\mathbb{N}_0$ may be used when the 0 being present is important.	$\mathbb{N}_+$ $\mathbb{N}_0$
$\mathbb{N}_+$	current	Used if it is important to consider the naturals as the set $\{1,2,\ldots\}$, it's also an example of why the notation $\mathbb{R}_+$ is bad (as some authors use $\mathbb{R}_+:=\{x\in\mathbb{R}\ \vert\ x\ge 0\}$ here it is being used for $>0$)	$\mathbb{N}_0$
$\mathbb{N}_0$	current	Used if it is important to consider the naturals as the set $\{0,1,\ldots\}$	$\mathbb{N}_+$