Real Numbers Symbol (ℝ): Meaning, Number Sets and LaTeX
July 24, 2026
The symbol for all real numbers is ℝ — a capital R in blackboard bold, the double-struck style used for number sets. It covers every number on the number line: integers, fractions and irrationals like π and √2. Copy it below, or jump to how to type it.
| Character | Unicode | HTML entity | LaTeX | Windows alt code |
|---|---|---|---|---|
| ℝ real numbers | U+211D | ℝ | \mathbb{R} | — |
| ℤ integers | U+2124 | ℤ | \mathbb{Z} | — |
The number sets and how they nest
| Where | Meaning |
|---|---|
| ℕ | Natural numbers — 0, 1, 2, 3, … (or from 1, by convention) |
| ℤ | Integers — the naturals plus their negatives |
| ℚ | Rationals — anything expressible as a fraction of integers |
| ℝ | Reals — the rationals plus irrationals like π, e and √2 |
| ℂ | Complex numbers — a + bi, with a and b real |
Each set contains the one before it
The number systems nest strictly: every integer is a rational, every rational is a real, every real is a complex number with zero imaginary part. The letters are not arbitrary — ℤ is from the German Zahlen (numbers), ℚ from quotient.
Writing domains and ranges
ℝ is how you say “all real numbers” compactly. Superscripts give dimension — ℝ² is the plane, ℝⁿ is n-dimensional space — and a union carves out excluded points.
Common decorations: ℝ⁺ for the positive reals, ℝ* or ℝ\{0} for the reals without zero. Conventions differ between texts, so define yours once.
What makes the reals different from the rationals
The reals are complete: every set that is bounded above has a least upper bound. The rationals fail this — the set of rationals whose square is under 2 has no rational least upper bound, because √2 is irrational. That gap is why calculus is built on ℝ.
How to type it
Windows
- In Word, type
211Dand pressAlt + Xfor ℝ - The other sets:
2115ℕ,2124ℤ,211Aℚ,2102ℂ - Elsewhere, press
Windows + .and search “double-struck”
Mac
- Open Character Viewer with
Control + Command + Spaceand search “double-struck capital R”
HTML
ℝorℝfor ℝℤℤ,ℚℚ,ℂℂ
In LaTeX
\mathbb{R} needs the amssymb package — without it you get an undefined control sequence. This is the single most common reason a blackboard-bold R fails to compile.
\mathbb only has capitals. There is no blackboard bold lowercase in the standard fonts, so \mathbb{r} will not give you what you expect.
Frequently asked questions
What is the symbol for all real numbers?
ℝ — a capital R in blackboard bold (U+211D). In LaTeX it is \mathbb{R} with the amssymb package.
What is the difference between ℝ and ℚ?
ℚ is the rationals — numbers writable as a fraction of integers. ℝ adds the irrationals such as π, e and √2, which cannot be written that way.
Why is my \mathbb{R} not working?
You are missing \usepackage{amssymb} in the preamble. Without it LaTeX has no \mathbb command and reports an undefined control sequence.
See also the union symbol used in interval notation, the epsilon symbol, and vector spaces in LaTeX.
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