View source for Blackboard bold

== Usage ==
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<!--'Blackboard bold letters used in mathematics' redirects here-->
The following table shows all available Unicode blackboard bold characters.{{r|w3c}}

The first column shows the letter as typically rendered by the [[LaTeX]] markup system. The second column shows the Unicode code point. The third column shows the Unicode symbol itself (which will only display correctly on browsers that support Unicode and have access to a suitable typeface). The fourth column describes some typical usage in mathematical texts.{{r|weisstein}} Some of the symbols (particularly <math>\mathbb{C}, \mathbb{Q}, \mathbb{R}</math> and <math>\mathbb{Z}</math>) are nearly universal in their interpretation,{{r|krantz}} while others are more varied in use.

{| class=wikitable style="max-width:50em;"
! scope="col" style="width: 4em;" | LaTeX
! scope="col" style="width: 6.5em;" | Unicode code point {{nobold|1=(hex)}}
! scope="col" style="width: 4em;" | Unicode symbol
! Mathematics usage
|-
! colspan="4" | Uppercase Latin
|-
|<math>\mathbb{A}</math>
|<code>U+1D538</code>
|style="font-size: 105%"|{{not a typo|𝔸}}
|Represents [[affine space]], <math>\mathbb{A}^n</math>, or the [[adele ring|ring of adeles]]. Occasionally represents the [[algebraic number]]s,{{r|sevryuk}} the [[algebraic closure]] of <math>\mathbb{Q}</math> (more commonly written <math>\overline{\mathbb{Q}}</math> or {{math|{{overline|'''Q'''}}}}), or the [[algebraic integer]]s, an important subring of the algebraic numbers.
|-
|<math>\mathbb{B}</math>
|<code>U+1D539</code>
|style="font-size: 105%"|{{not a typo|𝔹}}
|Sometimes represents a [[ball (mathematics)|ball]], a [[boolean domain]], or the [[Brauer group]] of a field.
|-
|<math>\mathbb{C}</math>
|<code>U+2102</code>
|style="font-size: 105%"|{{not a typo|ℂ}}
|Represents the [[set (mathematics)|set]] of [[complex number]]s.{{r|krantz}}
|-
|<math>\mathbb{D}</math>
|<code>U+1D53B</code>
|style="font-size: 105%"|{{not a typo|𝔻}}
|Represents the [[unit disk]] in the [[complex plane]], for example as the [[Poincaré disk model|conformal disk model]] of the [[hyperbolic plane]]. By generalisation <math>\mathbb{D}^n</math> may mean the {{mvar|n}}-dimensional [[ball (mathematics)|ball]]. Occasionally <math>\mathbb{D}</math> may mean the decimal fractions (see [[number]]), [[split-complex number]]s, or [[domain of discourse]].
|-
|<math>\mathbb{E}</math>
|<code>U+1D53C</code>
|style="font-size: 105%"|{{not a typo|𝔼}}
|Represents the [[expected value]] of a [[random variable]], or [[Euclidean space]], or a [[Field (mathematics)|field]] in a [[tower of fields]], or the [[Eudoxus reals]]. 
|-
|<math>\mathbb{F}</math>
|<code>U+1D53D</code>
|style="font-size: 105%"|{{not a typo|𝔽}}
|Represents a [[Field (mathematics)|field]].{{r|sevryuk}}  Often used for [[finite field]]s, with a subscript to indicate the order.{{r|sevryuk}}  Also represents a [[Hirzebruch surface]] or a [[free group]], with a subscript to indicate the number of generators (or generating set, if infinite).
|-
|<math>\mathbb{G}</math>
|<code>U+1D53E</code>
|style="font-size: 105%"|{{not a typo|𝔾}}
|Represents a [[Grassmannian]] or a [[group (mathematics)|group]], especially an [[algebraic group]] or [[group scheme]].
|-
|<math>\mathbb{H}</math>
|<code>U+210D</code>
|style="font-size: 105%"|{{not a typo|ℍ}}
|Represents the [[quaternion]]s (the H stands for [[William Rowan Hamilton|Hamilton]]),{{r|sevryuk}} or the [[upper half-plane]], or [[hyperbolic space]],{{r|sevryuk}} or [[hyperhomology]] of a complex.
|-
|<math>\mathbb{I}</math>
|<code>U+1D540</code>
|style="font-size: 105%"|{{not a typo|𝕀}}
|The closed [[unit interval]] or the [[Ideal (ring theory)|ideal]] of [[polynomial]]s vanishing on a [[subset]]. Occasionally the [[identity function|identity mapping]] on an [[algebraic structure]], or an [[indicator function]]. The set of purely [[imaginary numbers]] (i.e., the set of all real multiples of the [[imaginary unit]]).
|-
|<math>\mathbb{J}</math>
|<code>U+1D541</code>
|style="font-size: 105%"|{{not a typo|𝕁}}
|
|-
|<math>\mathbb{K}</math>
|<code>U+1D542</code>
|style="font-size: 105%"|{{not a typo|𝕂}}
|Represents a [[Field (mathematics)|field]],{{r|sevryuk}} K standing for [[German language|German]] {{lang|de|Körper}} (literally, 'body'; cf. French {{lang|fr|corps}} meaning 'body' or algebraic 'field').  May also denote a [[compact space]].
|-
|<math>\mathbb{L}</math>
|<code>U+1D543</code>
|style="font-size: 105%"|{{not a typo|𝕃}}
|Represents the Lefschetz motive. See [[Motive (algebraic geometry)]].
|-
|<math>\mathbb{M}</math>
|<code>U+1D544</code>
|style="font-size: 105%"|{{not a typo|𝕄}}
|Sometimes represents the [[monster group]]. The set of all {{nowrap|{{mvar|m}}-by-{{mvar|n}}}} [[Matrix (mathematics)|matrices]] is sometimes denoted  <math>\mathbb{M}(m, n)</math>. In [[geometric algebra]], represents the motor group of rigid motions. In [[functional programming]] and [[formal semantics (linguistics)|formal semantics]], denotes the type constructor for a [[monad (functional programming)|monad]].
|-
|<math>\mathbb{N}</math>
|<code>U+2115</code>
|style="font-size: 105%"|{{not a typo|ℕ}}
|Represents the set of [[natural number]]s.{{r|iso}} May or may not include [[0 (number)|zero]].
|-
|<math>\mathbb{O}</math>
|<code>U+1D546</code>
|style="font-size: 105%"|{{not a typo|𝕆}}
|Represents the [[octonion]]s.{{r|sevryuk}}
|-
|<math>\mathbb{P}</math>
|<code>U+2119</code>
|style="font-size: 105%"|{{not a typo|ℙ}}
|Represents [[projective space]], the [[probability]] of an event,{{r|sevryuk}} the [[prime number]]s,{{r|iso}} a [[power set]], the positive reals, the [[irrational numbers]], or a [[forcing (mathematics)|forcing]] [[partially ordered set|poset]].
|-
|<math>\mathbb{Q}</math>
|<code>U+211A</code>
|style="font-size: 105%"|{{not a typo|ℚ}}
|Represents the set of [[rational number]]s,{{r|krantz}} Q standing for [[quotient]]. With a prime number subscript {{mvar|p}}, represents the field of [[p-adic numbers|{{mvar|p}}-adic numbers]].
|-
|<math>\mathbb{R}</math>
|<code>U+211D</code>
|style="font-size: 105%"|{{not a typo|ℝ}}
|Represents the set of [[real number]]s.{{r|krantz}}
|-
|<math>\mathbb{S}</math>
|<code>U+1D54A</code>
|style="font-size: 105%"|{{not a typo|𝕊}}
|Represents a [[sphere]], or the [[sphere spectrum]], or occasionally the [[sedenion]]s.
|-
|<math>\mathbb{T}</math>
|<code>U+1D54B</code>
|style="font-size: 105%"|{{not a typo|𝕋}}
|Represents  the [[circle group]], particularly the [[unit circle]] in the complex plane (and <math>\mathbb{T}^n</math> the {{mvar|n}}-dimensional [[torus]]). Occasionally the [[trigintaduonion]]s, or a [[classical Hecke algebra|Hecke algebra]] (Hecke denoted his operators as {{math|''T''{{sub|''n''}}}} or <math>\mathbb{T}_n</math>), or the [[tropical semiring]], or [[twistor space]].
|-
|<math>\mathbb{U}</math>
|<code>U+1D54C</code>
|style="font-size: 105%"|{{not a typo|𝕌}}
|
|-
|<math>\mathbb{V}</math>
|<code>U+1D54D</code>
|style="font-size: 105%"|{{not a typo|𝕍}}
|Represents a [[vector space]] or an [[affine variety]] generated by a set of polynomials, or [[variance]] of a random variable.
|-
|<math>\mathbb{W}</math>
|<code>U+1D54E</code>
|style="font-size: 105%"|{{not a typo|𝕎}}
|Represents the [[natural number|whole numbers]] (here in the sense of non-negative integers), which also are represented by <math>\mathbb{N}_0</math>.
|-
|<math>\mathbb{X}</math>
|<code>U+1D54F</code>
|style="font-size: 105%"|{{not a typo|𝕏}}
|Occasionally used to denote an arbitrary [[metric space]].
|-
|<math>\mathbb{Y}</math>
|<code>U+1D550</code>
|style="font-size: 105%"|{{not a typo|𝕐}}
|
|-
|<math>\mathbb{Z}</math>
|<code>U+2124</code>
|style="font-size: 105%"|{{not a typo|ℤ}}
|Represents the set of [[integer]]s,{{r|krantz}} Z standing for German {{lang|de|Zahl}} (number). With a positive integer subscript {{mvar|n}}, it can mean the ring of [[modular arithmetic]] modulo {{mvar|n}}, or its additive [[cyclic group]] of order {{mvar|n}}; or with a prime subscript {{mvar|p}}, it can mean the ring of [[p-adic integers|{{mvar|p}}-adic integers]].
|-
! colspan="4" |Lowercase Latin
|-
| rowspan="10" |{{efn|name=latex|LaTeX renderings on this table are only available for uppercase Roman letters because [[Wikipedia]]'s implementation uses the [[AMSFonts]] blackboard bold typeface, which does not support other characters, and because LaTeX blackboard bold currently does not work with numerals due [[phab:T279805|a MediaWiki rendering bug]].}}
|<code>U+1D552</code>
|style="font-size: 105%"|{{not a typo|𝕒}}
|
|-
|<code>U+1D553</code>
|style="font-size: 105%"|{{not a typo|𝕓}}
|
|-
|<code>U+1D554</code>
|style="font-size: 105%"|{{not a typo|𝕔}}
|
|-
|<code>U+1D555</code>
|style="font-size: 105%"|{{not a typo|𝕕}}
|
|-
|<code>U+1D556</code>
|style="font-size: 105%"|{{not a typo|𝕖}}
|
|-
|<code>U+1D557</code>
|style="font-size: 105%"|{{not a typo|𝕗}}
|
|-
|<code>U+1D558</code>
|style="font-size: 105%"|{{not a typo|𝕘}}
|
|-
|<code>U+1D559</code>
|style="font-size: 105%"|{{not a typo|𝕙}}
|
|-
|<code>U+1D55A</code>
|style="font-size: 105%"|{{not a typo|𝕚}}
|Sometimes used to represent the [[imaginary unit]].<ref>{{cite conference|first=Stephen|last=Wolfram|author-link=Stephen Wolfram|year=2000|url=https://www.stephenwolfram.com/publications/mathematical-notation-past-future/|contribution=Mathematical Notation: Past and Future|type=Transcript of keynote address|title=MathML and Math on the Web: MathML International Conference 2000 |access-date=2025-04-08}}</ref>
|-
|<code>U+1D55B</code>
|style="font-size: 105%"|{{not a typo|𝕛}}
|
|-
|<math>\mathbb{k}</math>
|<code>U+1D55C</code>
|style="font-size: 105%"|{{not a typo|𝕜}}
|Represents a [[field (mathematics)|field]].
|-
| rowspan="15" |{{efn|name=latex}}
|<code>U+1D55D</code>
|style="font-size: 105%"|{{not a typo|𝕝}}
|
|-
|<code>U+1D55E</code>
|style="font-size: 105%"|{{not a typo|𝕞}}
|
|-
|<code>U+1D55F</code>
|style="font-size: 105%"|{{not a typo|𝕟}}
|
|-
|<code>U+1D560</code>
|style="font-size: 105%"|{{not a typo|𝕠}}
|
|-
|<code>U+1D561</code>
|style="font-size: 105%"|{{not a typo|𝕡}}
|
|-
|<code>U+1D562</code>
|style="font-size: 105%"|{{not a typo|𝕢}}
|
|-
|<code>U+1D563</code>
|style="font-size: 105%"|{{not a typo|𝕣}}
|
|-
|<code>U+1D564</code>
|style="font-size: 105%"|{{not a typo|𝕤}}
|
|-
|<code>U+1D565</code>
|style="font-size: 105%"|{{not a typo|𝕥}}
|
|-
|<code>U+1D566</code>
|style="font-size: 105%"|{{not a typo|𝕦}}
|
|-
|<code>U+1D567</code>
|style="font-size: 105%"|{{not a typo|𝕧}}
|
|-
|<code>U+1D568</code>
|style="font-size: 105%"|{{not a typo|𝕨}}
|
|-
|<code>U+1D569</code>
|style="font-size: 105%"|{{not a typo|𝕩}}
|
|-
|<code>U+1D56A</code>
|style="font-size: 105%"|{{not a typo|𝕪}}
|
|-
|<code>U+1D56B</code>
|style="font-size: 105%"|{{not a typo|𝕫}}
|
|-
! colspan="4" |Italic Latin
|-
| rowspan="5" |{{efn|name=latex}}
|<code>U+2145</code>
|style="font-size: 105%"|{{not a typo|ⅅ}}
|
|-
|<code>U+2146</code>
|style="font-size: 105%"|{{not a typo|ⅆ}}
|
|-
|<code>U+2147</code>
|style="font-size: 105%"|{{not a typo|ⅇ}}
|
|-
|<code>U+2148</code>
|style="font-size: 105%"|{{not a typo|ⅈ}}
|
|-
|<code>U+2149</code>
|style="font-size: 105%"|{{not a typo|ⅉ}}
|
|-
! colspan="4" |Greek
|-
| rowspan="5" |{{efn|name=latex}}
|<code>U+213E</code>
|style="font-size: 105%"|{{not a typo|ℾ}}
|
|-
|<code>U+213D</code>
|style="font-size: 105%"|{{not a typo|ℽ}}
|
|-
|<code>U+213F</code>
|style="font-size: 105%"|{{not a typo|ℿ}}
|
|-
|<code>U+213C</code>
|style="font-size: 105%"|{{not a typo|ℼ}}
|
|-
|<code>U+2140</code>
|style="font-size: 105%"|{{not a typo|⅀}}
|
|-
! colspan="4" |Digits
|-
| rowspan="10" |{{efn|name=latex}}
|<code>U+1D7D8</code>
|style="font-size: 105%"|{{not a typo|𝟘}}
|In algebra of logical propositions, it represents a contradiction or falsity.
|-
|<code>U+1D7D9</code>
|style="font-size: 105%"|{{not a typo|𝟙}}
|In [[set theory]], the [[Greatest element|top element]] of a [[forcing (mathematics)|forcing]] [[partially ordered set|poset]], or occasionally the identity matrix in a [[matrix ring]]. Also used for the [[indicator function]] and the [[unit step function]], and for the [[identity function|identity operator]] or [[identity matrix]]. In [[geometric algebra]], represents the unit antiscalar, the identity element under the geometric antiproduct. In algebra of logical propositions, it represents a tautology.
|-
|<code>U+1D7DA</code>
|style="font-size: 105%"|{{not a typo|𝟚}}
|In [[category theory]], the interval category.
|-
|<code>U+1D7DB</code>
|style="font-size: 105%"|{{not a typo|𝟛}}
|
|-
|<code>U+1D7DC</code>
|style="font-size: 105%"|{{not a typo|𝟜}}
|
|-
|<code>U+1D7DD</code>
|style="font-size: 105%"|{{not a typo|𝟝}}
|
|-
|<code>U+1D7DE</code>
|style="font-size: 105%"|{{not a typo|𝟞}}
|
|-
|<code>U+1D7DF</code>
|style="font-size: 105%"|{{not a typo|𝟟}}
|
|-
|<code>U+1D7E0</code>
|style="font-size: 105%"|{{not a typo|𝟠}}
|
|-
|<code>U+1D7E1</code>
|style="font-size: 105%"|{{not a typo|𝟡}}
|
|-
! colspan="4" |Arabic
|-
| rowspan="25" |{{efn|name=latex}}
|<code>U+1EEA1</code>
|style="font-size: 105%"|{{not a typo|𞺡}}
|
|-
|<code>U+1EEA2</code>
|style="font-size: 105%"|{{not a typo|𞺢}}
|
|-
|<code>U+1EEA3</code>
|style="font-size: 105%"|{{not a typo|𞺣}}
|
|-
|<code>U+1EEA5</code>
|style="font-size: 105%"|{{not a typo|𞺥}}
|
|-
|<code>U+1EEA6</code>
|style="font-size: 105%"|{{not a typo|𞺦}}
|
|-
|<code>U+1EEA7</code>
|style="font-size: 105%"|{{not a typo|𞺧}}
|
|-
|<code>U+1EEA8</code>
|style="font-size: 105%"|{{not a typo|𞺨}}
|
|-
|<code>U+1EEA9</code>
|style="font-size: 105%"|{{not a typo|𞺩}}
|
|-
|<code>U+1EEAB</code>
|style="font-size: 105%"|{{not a typo|𞺫}}
|
|-
|<code>U+1EEAC</code>
|style="font-size: 105%"|{{not a typo|𞺬}}
|
|-
|<code>U+1EEAD</code>
|style="font-size: 105%"|{{not a typo|𞺭}}
|
|-
|<code>U+1EEAE</code>
|style="font-size: 105%"|{{not a typo|𞺮}}
|
|-
|<code>U+1EEAF</code>
|style="font-size: 105%"|{{not a typo|𞺯}}
|
|-
|<code>U+1EEB0</code>
|style="font-size: 105%"|{{not a typo|𞺰}}
|
|-
|<code>U+1EEB1</code>
|style="font-size: 105%"|{{not a typo|𞺱}}
|
|-
|<code>U+1EEB2</code>
|style="font-size: 105%"|{{not a typo|𞺲}}
|
|-
|<code>U+1EEB3</code>
|style="font-size: 105%"|{{not a typo|𞺳}}
|
|-
|<code>U+1EEB4</code>
|style="font-size: 105%"|{{not a typo|𞺴}}
|
|-
|<code>U+1EEB5</code>
|style="font-size: 105%"|{{not a typo|𞺵}}
|
|-
|<code>U+1EEB6</code>
|style="font-size: 105%"|{{not a typo|𞺶}}
|
|-
|<code>U+1EEB7</code>
|style="font-size: 105%"|{{not a typo|𞺷}}
|
|-
|<code>U+1EEB8</code>
|style="font-size: 105%"|{{not a typo|𞺸}}
|
|-
|<code>U+1EEB9</code>
|style="font-size: 105%"|{{not a typo|𞺹}}
|
|-
|<code>U+1EEBA</code>
|style="font-size: 105%"|{{not a typo|𞺺}}
|
|-
|<code>U+1EEBB</code>
|style="font-size: 105%"|{{not a typo|𞺻}}
|
|}

In addition, a blackboard-bold {{math|'''[[mu (letter)|μ]]'''{{sub|''n''}}}} (not found in Unicode or {{code|amsmath}} LaTeX) is sometimes used by [[number theory|number theorists]] and [[algebraic geometry|algebraic geometers]] to designate the [[group scheme]] of {{nowrap|{{mvar|n}}-th}} [[roots of unity]].{{r|milne}}