Index of notation/N
From Maths
Expression  Status  Meanings  See also 

[ilmath]\mathbb{N} [/ilmath]  current  The natural number (or naturals), either [ilmath]\mathbb{N}:=\{0,1,\ldots,n,\ldots\}[/ilmath] or [ilmath]\mathbb{N}:=\{1,2,\ldots,n,\ldots\}[/ilmath]. In contexts where starting from one actually matters [ilmath]\mathbb{N}_+[/ilmath] is used, usually it is clear from the context, [ilmath]\mathbb{N}_0[/ilmath] may be used when the 0 being present is important. 

[ilmath]\mathbb{N}_+[/ilmath]  current  Used if it is important to consider the naturals as the set [ilmath]\{1,2,\ldots\} [/ilmath], it's also an example of why the notation [ilmath]\mathbb{R}_+[/ilmath] is bad (as some authors use [ilmath]\mathbb{R}_+:=\{x\in\mathbb{R}\ \vert\ x\ge 0\}[/ilmath] here it is being used for [ilmath]>0[/ilmath]) 

[ilmath]\mathbb{N}_0[/ilmath]  current  Used if it is important to consider the naturals as the set [ilmath]\{0,1,\ldots\} [/ilmath] 
