# Symbol for the set of odd naturals?

Obviously the set of naturals is denoted $\mathbb{N}$, but is there a symbol for the set of odd naturals? Would $2\mathbb{N}+1$ (or $2\mathbb{N}-1$) be a standard notation?

• $\:2\,\Bbb N + 1\:$ and $\:2\,\Bbb Z + 1\:$ are frequently emploed in number theory and algebra. Sep 29, 2012 at 22:03

I don't recall seeing too many places that gave a specific notation to the set of even or odd numbers. Your notation of $2\mathbb N+1$ seems quite reasonable.
Let $\mathbb O$ denote the set of positive odd integers.
How about $\mathbb{N}\setminus2\mathbb{N}$ ?
Why not $\{2n-1,\;n\in\mathbb{N}\}?$ Or are you looking for an actual symbol? I recall seeing $\mathbb{E}$ and $\mathbb{O}$ somewhere - (of course, specify what you mean if you use the $\mathbb{E}$'s $\mathbb{O}$'s $\mathbb{P}$'s etc. in a paper).
• $\{2n-1, \ \forall n \in \mathbb N\}$ is extremely untidy, if it means anything at all. You might say $\{2n-1:n \in \mathbb N\}$ or $\{2n-1\ |\ n \in \mathbb N\}$, depending on convention. Sep 29, 2012 at 23:07