This site is supported by donations to The OEIS Foundation.

Blackboard bold

From OeisWiki
Jump to: navigation, search

This article is under construction.

Please do not rely on any information it contains.

A blackboard bold (double struck, open face) letter is an uppercase alphabetic character of the Latin alphabet that denotes an important set of numbers. Although the entire alphabet is available for this purpose in LaTeX and many of them have been assigned at one time or another, only a few letters are regularly used as blackboard bold in number theory, namely
for natural numbers,
for rational integers,
for rational numbers,
for algebraic numbers,
for real numbers, and
for complex numbers. Many texts also use
to denote a finite field with
elements ( 
generally specified to be a prime number).


LaTeX text style
Code Result
<math>\scriptstyle \mathbb{N},\, \N</math>
<math>\scriptstyle \mathbb{Z},\, \Z</math>
<math>\scriptstyle \mathbb{Q},\, \Q</math>
<math>\scriptstyle \mathbb{R},\, \R</math>
<math>\scriptstyle \mathbb{C},\, \C</math>
LaTeX display style
Code Result
<math>\mathbb{N}, \N</math>
<math>\mathbb{Z}, \Z</math>
<math>\mathbb{Q}, \Q</math>
<math>\mathbb{R}, \R</math>
<math>\mathbb{C}, \C</math>
LaTeX text style
Code Result
{{math|{{mathbb|N|tex}},\, {{sym|N|tex}}|$}}
{{math|{{mathbb|Z|tex}},\, {{sym|Z|tex}}|$}}
{{math|{{mathbb|Q|tex}},\, {{sym|Q|tex}}|$}}
{{math|{{mathbb|R|tex}},\, {{sym|R|tex}}|$}}
{{math|{{mathbb|C|tex}},\, {{sym|C|tex}}|$}}
LaTeX display style
Code Result
{{math|{{mathbb|N|tex}}, {{sym|N|tex}}|$$}}
{{math|{{mathbb|Z|tex}}, {{sym|Z|tex}}|$$}}
{{math|{{mathbb|Q|tex}}, {{sym|Q|tex}}|$$}}
{{math|{{mathbb|R|tex}}, {{sym|R|tex}}|$$}}
{{math|{{mathbb|C|tex}}, {{sym|C|tex}}|$$}}


HTML+CSS text style
Code Result
{{math|{{mathbb|N}}, {{sym|N}}|&}}
ℕ, ℕ
{{math|{{mathbb|Z}}, {{sym|Z}}|&}}
ℤ, ℤ
{{math|{{mathbb|Q}}, {{sym|Q}}|&}}
ℚ, ℚ
{{math|{{mathbb|R}}, {{sym|R}}|&}}
ℝ, ℝ
{{math|{{mathbb|C}}, {{sym|C}}|&}}
ℂ, ℂ
HTML+CSS display style
Code Result
{{math|{{mathbb|N}}, {{sym|N}}|&&}}
ℕ, ℕ
{{math|{{mathbb|Z}}, {{sym|Z}}|&&}}
ℤ, ℤ
{{math|{{mathbb|Q}}, {{sym|Q}}|&&}}
ℚ, ℚ
{{math|{{mathbb|R}}, {{sym|R}}|&&}}
ℝ, ℝ
{{math|{{mathbb|C}}, {{sym|C}}|&&}}
ℂ, ℂ


The following table shows all available Unicode blackboard bold characters. The first column shows the LaTeX markup code for the blackboard bold character. The second column shows the blackboard bold character as typically rendered by the ubiquitous LaTeX markup system. The third column shows the Unicode codepoint. The fourth column shows the HTML+CSS markup code for the blackboard bold character. The fifth column shows the blackboard bold character as typically rendered by the browser with HTML+CSS (which will only display correctly if your browser supports Unicode and has access to a suitable font). The fifth column describes known typical (but not universal) usage in mathematical texts.

Blackboard bold characters
Unicode (Hex) HTML+CSS
Mathematical usage
<math>\mathbb{A}</math> U+1D538 {{math|{{mathbb|A}}, {{Unicode|&#x1D538;}}|&&}}
𝔸, 𝔸
Represents affine space or the ring of adeles. Sometimes represents the algebraic numbers, the algebraic closure of (or Q), notated (although Q is often used instead). It may also represent the algebraic integers, an important subring of the algebraic numbers.
{{math|{\rm a}{{sp|-7|tex}}{\rm a}|$$}} U+1D552 {{math|{{mathbb|a}}, {{Unicode|&#x1D552;}}|&&}}
𝕒, 𝕒
<math>\mathbb{B}</math> U+1D539 {{math|{{mathbb|B}}, {{Unicode|&#x1D539;}}|&&}}
𝔹, 𝔹
Sometimes represents a ball, a boolean domain, or the Brauer group of a field.
{{math|{\rm b}{{sp|-7|tex}}{\rm b}|$$}} U+1D553 {{math|{{mathbb|b}}, {{Unicode|&#x1D553;}}|&&}}
𝕓, 𝕓
<math>\mathbb{C}</math> U+2102 {{math|{{mathbb|C}}, {{Unicode|&#x2102;}}|&&}}
Represents the complex numbers.
{{math|{\rm c}{{sp|-5|tex}}{\rm c}|$$}} U+1D554 {{math|{{mathbb|c}}, {{Unicode|&#x1D554;}}|&&}}
𝕔, 𝕔
<math>\mathbb{D}</math> U+1D53B {{math|{{mathbb|D}}, {{Unicode|&#x1D53B;}}|&&}}
𝔻, 𝔻
Represents the unit (open) disk in the complex plane (for example as a model of the Hyperbolic plane), or the decimal fractions (see number).
{{math|{\rm d}{{sp|-7|tex}}{\rm d}|$$}} U+1D555 {{math|{{mathbb|d}}, {{Unicode|&#x1D555;}}|&&}}
𝕕, 𝕕
{{math|D {{sp|-9|tex}}{{sp|-3|tex}} D|$$}} U+2145 {{math|''{{mathbb|D}}'', {{Unicode|&#x2145;}}|&&}}
{{math|d{{sp|-7|tex}}d|$$}} U+2146 {{math|''{{mathbb|d}}'', {{Unicode|&#x2146;}}|&&}}
May represent the differential symbol.
<math>\mathbb{E}</math> U+1D53C {{math|{{mathbb|E}}, {{Unicode|&#x1D53C;}}|&&}}
𝔼, 𝔼
Represents the expected value of a random variable, or Euclidean space, or a field in a tower of fields.
{{math|{\rm e}{{sp|-5|tex}}{\rm e}|$$}} U+1D556 {{math|{{mathbb|e}}, {{Unicode|&#x1D556;}}|&&}}
𝕖, 𝕖
{{math|e{{sp|-6|tex}}e|$$}} U+2147 {{math|''{{mathbb|e}}'', {{Unicode|&#x2147;}}|&&}}
Sometimes used for the Euler's number e.
<math>\mathbb{F}</math> U+1D53D {{math|{{mathbb|F}}, {{Unicode|&#x1D53D;}}|&&}}
𝔽, 𝔽
Represents a field. Often used for finite fields, with a subscript to indicate the order. Also represents a Hirzebruch surface or a free group, with a subset to indicate the number of generators (or generating set, if infinite).
{{math|{\rm f}{{sp|-4|tex}}{\rm f}|$$}} U+1D557 {{math|{{mathbb|f}}, {{Unicode|&#x1D557;}}|&&}}
𝕗, 𝕗
<math>\mathbb{G}</math> U+1D53E {{math|{{mathbb|G}}, {{Unicode|&#x1D53E;}}|&&}}
𝔾, 𝔾
Represents a Grassmannian or a group, especially an algebraic group.
{{math|{\rm g}{{sp|-7|tex}}{\rm g}|$$}} U+1D558 {{math|{{mathbb|g}}, {{Unicode|&#x1D558;}}|&&}}
𝕘, 𝕘
<math>\mathbb{H}</math> U+210D {{math|{{mathbb|H}}, {{Unicode|&#x210D;}}|&&}}
Represents the quaternions (the H stands for Hamilton), or the upper half-plane, or hyperbolic space, or hyperhomology of a complex.
{{math|{\rm h}{{sp|-7|tex}}{\rm h}|$$}} U+1D559 {{math|{{mathbb|h}}, {{Unicode|&#x1D559;}}|&&}}
𝕙, 𝕙
<math>\mathbb{I}</math> U+1D540 {{math|{{mathbb|I}}, {{Unicode|&#x1D540;}}|&&}}
𝕀, 𝕀
Occasionally used to denote the identity mapping on an algebraic structure, or the set of imaginary numbers (i.e., the set of all real multiples of the imaginary unit).
{{math|{\rm i}{{sp|-2|tex}}{\rm i}|$$}} U+1D55A {{math|{{mathbb|i}}, {{Unicode|&#x1D55A;}}|&&}}
𝕚, 𝕚
{{math|i{{sp|-3|tex}}i|$$}} U+2148 {{math|''{{mathbb|i}}'', {{Unicode|&#x2148;}}|&&}}
Occasionally used for the imaginary unit.
<math>\mathbb{J}</math> U+1D541 {{math|{{mathbb|J}}, {{Unicode|&#x1D541;}}|&&}}
𝕁, 𝕁
Sometimes represents the irrational numbers, R\Q (ℝ\ℚ).
{{math|{\rm j}{{sp|-3|tex}}{\rm j}|$$}} U+1D55B {{math|{{mathbb|j}}, {{Unicode|&#x1D55B;}}|&&}}
𝕛, 𝕛
{{math|j{{sp|-5|tex}}j|$$}} U+2149 {{math|''{{mathbb|j}}'', {{Unicode|&#x2149;}}|&&}}
<math>\mathbb{K}</math> U+1D542 {{math|{{mathbb|K}}, {{Unicode|&#x1D542;}}|&&}}
𝕂, 𝕂
Represents a field, typically a scalar field. This is derived from the German word Körper, which means field (literally, "body"; cf. the French term corps). May also be used to denote a compact space.
{{math|{\rm k}{{sp|-7|tex}}{\rm k}|$$}} U+1D55C {{math|{{mathbb|k}}, {{Unicode|&#x1D55C;}}|&&}}
𝕜, 𝕜
<math>\mathbb{L}</math> U+1D543 {{math|{{mathbb|L}}, {{Unicode|&#x1D543;}}|&&}}
𝕃, 𝕃
Represents the Lefschetz motive. (See motives.)
{{math|{\rm l}{{sp|-2|tex}}{\rm l}|$$}} U+1D55D {{math|{{mathbb|l}}, {{Unicode|&#x1D55D;}}|&&}}
𝕝, 𝕝
<math>\mathbb{M}</math> U+1D544 {{math|{{mathbb|M}}, {{Unicode|&#x1D544;}}|&&}}
𝕄, 𝕄
Represents the monster group.
{{math|{\rm m}{{sp|-9|tex}}{{sp|-4|tex}}{\rm m}|$$}} U+1D55E {{math|{{mathbb|m}}, {{Unicode|&#x1D55E;}}|&&}}
𝕞, 𝕞
<math>\mathbb{N}</math> U+2115 {{math|{{mathbb|N}}, {{Unicode|&#x2115;}}|&&}}
Represents the natural numbers. (May or may not include zero.)
{{math|{\rm n}{{sp|-8|tex}}{\rm n}|$$}} U+1D55F {{math|{{mathbb|n}}, {{Unicode|&#x1D55F;}}|&&}}
𝕟, 𝕟
<math>\mathbb{O}</math> U+1D546 {{math|{{mathbb|O}}, {{Unicode|&#x1D546;}}|&&}}
𝕆, 𝕆
Represents the octonions.
{{math|{\rm o}{{sp|-6|tex}}{\rm o}|$$}} U+1D560 {{math|{{mathbb|o}}, {{Unicode|&#x1D560;}}|&&}}
𝕠, 𝕠
<math>\mathbb{P}</math> U+2119 {{math|{{mathbb|P}}, {{Unicode|&#x2119;}}|&&}}
Represents projective space, the probability of an event, the prime numbers, a power set, the positive reals, the irrational numbers, or a forcing partially ordered set (poset).
{{math|{\rm p}{{sp|-7|tex}}{\rm p}|$$}} U+1D561 {{math|{{mathbb|p}}, {{Unicode|&#x1D561;}}|&&}}
𝕡, 𝕡
<math>\mathbb{Q}</math> U+211A {{math|{{mathbb|Q}}, {{Unicode|&#x211A;}}|&&}}
Represents the rational numbers. (The Q stands for quotient.)
{{math|{\rm q}{{sp|-7|tex}}{\rm q}|$$}} U+1D562 {{math|{{mathbb|q}}, {{Unicode|&#x1D562;}}|&&}}
𝕢, 𝕢
<math>\mathbb{R}</math> U+211D {{math|{{mathbb|R}}, {{Unicode|&#x211D;}}|&&}}
Represents the real numbers.
{{math|{\rm r}{{sp|-4|tex}}{\rm r}|$$}} U+1D563 {{math|{{mathbb|r}}, {{Unicode|&#x1D563;}}|&&}}
𝕣, 𝕣
<math>\mathbb{S}</math> U+1D54A {{math|{{mathbb|S}}, {{Unicode|&#x1D54A;}}|&&}}
𝕊, 𝕊
Represents the sedenions, or a sphere.
{{math|{\rm s}{{sp|-5|tex}}{\rm s}|$$}} U+1D564 {{math|{{mathbb|s}}, {{Unicode|&#x1D564;}}|&&}}
𝕤, 𝕤
<math>\mathbb{T}</math> U+1D54B {{math|{{mathbb|T}}, {{Unicode|&#x1D54B;}}|&&}}
𝕋, 𝕋
Represents a torus, or the circle group or a Hecke algebra (Hecke denoted his operators as Tn or 𝕋𝕟), or the Tropical semi-ring.
{{math|{\rm t}{{sp|-4|tex}}{\rm t}|$$}} U+1D565 {{math|{{mathbb|t}}, {{Unicode|&#x1D565;}}|&&}}
𝕥, 𝕥
<math>\mathbb{U}</math> U+1D54C {{math|{{mathbb|U}}, {{Unicode|&#x1D54C;}}|&&}}
𝕌, 𝕌
{{math|{\rm u}{{sp|-8|tex}}{\rm u}|$$}} U+1D566 {{math|{{mathbb|u}}, {{Unicode|&#x1D566;}}|&&}}
𝕦, 𝕦
<math>\mathbb{V}</math> U+1D54D {{math|{{mathbb|V}}, {{Unicode|&#x1D54D;}}|&&}}
𝕍, 𝕍
Represents a vector space.
{{math|{\rm v}{{sp|-7|tex}}{\rm v}|$$}} U+1D567 {{math|{{mathbb|v}}, {{Unicode|&#x1D567;}}|&&}}
𝕧, 𝕧
<math>\mathbb{W}</math> U+1D54E {{math|{{mathbb|W}}, {{Unicode|&#x1D54E;}}|&&}}
𝕎, 𝕎
Represents the whole numbers (here in the sense of non-negative integers), which also are represented by 0.
{{math|{\rm w}{{sp|-9|tex}}{{sp|-2|tex}}{\rm w}|$$}} U+1D568 {{math|{{mathbb|w}}, {{Unicode|&#x1D568;}}|&&}}
𝕨, 𝕨
<math>\mathbb{X}</math> U+1D54F {{math|{{mathbb|X}}, {{Unicode|&#x1D54F;}}|&&}}
𝕏, 𝕏
Occasionally used to denote an arbitrary metric space.
{{math|{\rm x}{{sp|-7|tex}}{\rm x}|$$}} U+1D569 {{math|{{mathbb|x}}, {{Unicode|&#x1D569;}}|&&}}
𝕩, 𝕩
<math>\mathbb{Y}</math> U+1D550 {{math|{{mathbb|Y}}, {{Unicode|&#x1D550;}}|&&}}
𝕐, 𝕐
{{math|{\rm y}{{sp|-7|tex}}{\rm y}|$$}} U+1D56A {{math|{{mathbb|y}}, {{Unicode|&#x1D56A;}}|&&}}
𝕪, 𝕪
<math>\mathbb{Z}</math> U+2124 {{math|{{mathbb|Z}}, {{Unicode|&#x2124;}}|&&}}
Represents the integers. (The Z is for Zahlen, which is German for "numbers".)
{{math|{\rm z}{{sp|-5|tex}}{\rm z}|$$}} U+1D56B {{math|{{mathbb|z}}, {{Unicode|&#x1D56B;}}|&&}}
𝕫, 𝕫
{{math|\Gamma{{sp|-9|tex}}\Gamma|$$}} U+213E {{math|{{Unicode|ℾ}}, {{Unicode|&#x213E;}}|&&}}
{{math|\gamma{{sp|-9|tex}}\gamma|$$}} U+213D {{math|{{Unicode|ℽ}}, {{Unicode|&#x213D;}}|&&}}
{{math|\prod{{sp|-18|tex}}{{sp|-7|tex}}\prod|$$}} U+213F {{math|{{Unicode|ℿ}}, {{Unicode|&#x213F;}}|&&}}
{{math|\pi{{sp|-9|tex}}\pi|$$}} U+213C {{math|{{Unicode|ℼ}}, {{Unicode|&#x213C;}}|&&}}
{{math|\sum{{sp|-18|tex}}{{sp|-9|tex}}{{sp|-1|tex}}\sum|$$}} U+2140 {{math|{{Unicode|⅀}}, {{Unicode|&#x2140;}}|&&}}
{{math|0{{sp|-6|tex}}0|$$}} U+1D7D8 {{math|{{mathbb|0}}, {{Unicode|&#x1D7D8;}}|&&}}
𝟘, 𝟘
{{math|1{{sp|-6|tex}}1|$$}} U+1D7D9 {{math|{{mathbb|1}}, {{Unicode|&#x1D7D9;}}|&&}}
𝟙, 𝟙
Often represents, in set theory, the top element of a forcing partially ordered set (poset), or occasionally for the identity matrix in a matrix ring.
{{math|2{{sp|-6|tex}}2|$$}} U+1D7DA {{math|{{mathbb|2}}, {{Unicode|&#x1D7DA;}}|&&}}
𝟚, 𝟚
{{math|3{{sp|-6|tex}}3|$$}} U+1D7DB {{math|{{mathbb|3}}, {{Unicode|&#x1D7DB;}}|&&}}
𝟛, 𝟛
{{math|4{{sp|-6|tex}}4|$$}} U+1D7DC {{math|{{mathbb|4}}, {{Unicode|&#x1D7DC;}}|&&}}
𝟜, 𝟜
{{math|5{{sp|-6|tex}}5|$$}} U+1D7DD {{math|{{mathbb|5}}, {{Unicode|&#x1D7DD;}}|&&}}
𝟝, 𝟝
{{math|6{{sp|-6|tex}}6|$$}} U+1D7DE {{math|{{mathbb|6}}, {{Unicode|&#x1D7DE;}}|&&}}
𝟞, 𝟞
{{math|7{{sp|-6|tex}}7|$$}} U+1D7DF {{math|{{mathbb|7}}, {{Unicode|&#x1D7DF;}}|&&}}
𝟟, 𝟟
{{math|8{{sp|-6|tex}}8|$$}} U+1D7E0 {{math|{{mathbb|8}}, {{Unicode|&#x1D7E0;}}|&&}}
𝟠, 𝟠
{{math|9{{sp|-6|tex}}9|$$}} U+1D7E1 {{math|{{mathbb|9}}, {{Unicode|&#x1D7E1;}}|&&}}
𝟡, 𝟡

See also

  • {{mathbb}} (mathematical formatting template)