ℕ
ℕ Natural Numbers Symbol
ℕ is the set of natural numbers — the counting numbers. Whether it starts at 0 or at 1 depends on the author, which is why it is worth stating.
Also known as: natural numbers symbol, set of natural numbers, double struck n, counting numbers symbol.
Codes
| Symbol | ℕ | |
| Unicode | U+2115 | |
| HTML entity (named) | ℕ | |
| HTML entity (decimal) | ℕ | |
| HTML entity (hex) | ℕ | |
| CSS | \2115 | |
| LaTeX | \mathbb{N} | |
| Windows Alt code | Alt + 8469 |
How to type ℕ (Natural Numbers Symbol)
Windows2115, Alt + X
In Word, type 2115 then press Alt + X. Elsewhere, copy ℕ above or use Character Map (search “double-struck”).
Mac
No default keystroke. Open Character Viewer (Control + Cmd + Space) and search “double-struck capital N”, or copy ℕ above.
Microsoft Word2115, Alt + X
Type 2115, then press Alt + X to convert it to ℕ.
Google Docs
Insert → Equation, then type \N or \mathbb followed by N.
LaTeX\mathbb{N}
Use \mathbb{N} in math mode (requires amssymb or amsfonts).
Usage
- ℕ is the counting numbers: 1, 2, 3, … — or 0, 1, 2, 3, … depending on who is writing.
- Does ℕ include 0? There is no universal answer. Set theory and computer science usually say yes; number theory and much of analysis usually say no. Serious writing states the convention, or sidesteps it with ℕ₀ (with zero) and ℕ⁺ or ℤ⁺ (without).
- n ∈ ℕ constrains n to a counting number — the usual way to index a sequence or bound a loop in a proof.
- ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ: every natural number is an integer, every integer a rational, every rational a real.