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16.2 Math symbols ¶

LaTeX provides almost any mathematical or technical symbol that anyone uses. For example, if you include $\pi$ in your source, you will get the pi symbol π. See the “Comprehensive LaTeX Symbol List” package at https://ctan.org/pkg/comprehensive .

Here is a list of commonly-used symbols. It is by no means exhaustive. Each symbol is described with a short phrase, and its symbol class, which determines the spacing around it, is given in parenthesis. Unless said otherwise, the commands for these symbols can be used only in math mode. To redefine a command so that it can be used whatever the current mode, see \ensuremath .

∥ Parallel (relation). Synonym:  \parallel .

ℵ Aleph, transfinite cardinal (ordinary).

α Lowercase Greek letter alpha (ordinary).

⨿ Disjoint union (binary)

∠ Geometric angle (ordinary). Similar: less-than sign  < and angle bracket  \langle .

≈ Almost equal to (relation).

∗ Asterisk operator, convolution, six-pointed (binary). Synonym:  * , which is often a superscript or subscript, as in the Kleene star. Similar:  \star , which is five-pointed, and is sometimes used as a general binary operation, and sometimes reserved for cross-correlation.

≍ Asymptotically equivalent (relation).

\ Backslash (ordinary). Similar: set minus  \setminus , and \textbackslash for backslash outside of math mode.

β Lowercase Greek letter beta (ordinary).

⋂ Variable-sized, or n-ary, intersection (operator). Similar: binary intersection  \cap .

⚪ Circle, larger (binary). Similar: function composition  \circ .

⋃ Variable-sized, or n-ary, union (operator). Similar: binary union  \cup .

⨀ Variable-sized, or n-ary, circled dot operator (operator).

⨁ Variable-sized, or n-ary, circled plus operator (operator).

⨂ Variable-sized, or n-ary, circled times operator (operator).

▽ Variable-sized, or n-ary, open triangle pointing down (binary). Synonym: \varbigtriangledown .

△ Variable-sized, or n-ary, open triangle pointing up (binary). Synonym: \varbigtriangleup .

⨆ Variable-sized, or n-ary, square union (operator).

⨄ Variable-sized, or n-ary, union operator with a plus (operator). (Note that the name has only one p.)

⋁ Variable-sized, or n-ary, logical-or (operator).

⋀ Variable-sized, or n-ary, logical-and (operator).

⊥, Up tack, bottom, least element of a partially ordered set, or a contradiction (ordinary). See also  \top .

⋈ Natural join of two relations (relation).

□ Modal operator for necessity; square open box (ordinary). Not available in plain TeX. In LaTeX you need to load the amssymb package.

• Bullet (binary). Similar: multiplication dot  \cdot .

∩ Intersection of two sets (binary). Similar: variable-sized operator  \bigcap .

⋅ Multiplication (binary). Similar: Bullet dot  \bullet .

χ Lowercase Greek chi (ordinary).

∘ Function composition, ring operator (binary). Similar: variable-sized operator  \bigcirc .

♣ Club card suit (ordinary).

∁, Set complement, used as a superscript as in $S^\complement$ (ordinary). Not available in plain TeX. In LaTeX you need to load the amssymb package. Also used: $S^{\mathsf{c}}$ or  $\bar{S}$ .

≅ Congruent (relation).

∐ Coproduct (operator).

∪ Union of two sets (binary). Similar: variable-sized operator  \bigcup .

† Dagger relation (binary).

⊣ Dash with vertical, reversed turnstile (relation). Similar: turnstile  \vdash .

‡ Double dagger relation (binary).

Δ Greek uppercase delta, used for increment (ordinary).

δ Greek lowercase delta (ordinary).

◇ Large diamond operator (ordinary). Not available in plain TeX. In LaTeX you need to load the amssymb package.

⋄ Diamond operator (binary). Similar: large diamond  \Diamond , circle bullet  \bullet .

♢ Diamond card suit (ordinary).

÷ Division sign (binary).

≐ Approaches the limit (relation). Similar: geometrically equal to  \Doteq .

↓ Down arrow, converges (relation). Similar: \Downarrow double line down arrow.

⇓ Double line down arrow (relation). Similar: \downarrow single line down arrow.

ℓ Lowercase cursive letter l (ordinary).

∅ Empty set symbol (ordinary). The variant form is \varnothing .

ϵ Lowercase lunate epsilon (ordinary). Similar to Greek text letter. More widely used in mathematics is the script small letter epsilon \varepsilon  ε. Related: the set membership relation \in  ∈.

≡ Equivalence (relation).

η Lowercase Greek letter (ordinary).

∃ Existential quantifier (ordinary).

♭ Musical flat (ordinary).

∀ Universal quantifier (ordinary).

⌢ Downward curving arc (ordinary).

Γ uppercase Greek letter (ordinary).

γ Lowercase Greek letter (ordinary).

≥ Greater than or equal to (relation). This is a synonym for  \geq .

≥ Greater than or equal to (relation). This is a synonym for  \ge .

← Is assigned the value (relation). Synonym:  \leftarrow .

≫ Much greater than (relation). Similar: much less than  \ll .

ℏ Planck constant over two pi (ordinary).

♡ Heart card suit (ordinary).

↩ Hooked left arrow (relation).

↪ Hooked right arrow (relation).

⟷ If and only if (relation). It is \Longleftrightarrow with a \thickmuskip on either side.

ℑ Imaginary part (ordinary). See: real part  \Re .

Dotless i; used when you are putting an accent on an i (see Math accents ).

∈ Set element (relation). See also: lowercase lunate epsilon  \epsilon ϵ and small letter script epsilon  \varepsilon .

∞ Infinity (ordinary).

∫ Integral (operator).

ι Lowercase Greek letter (ordinary).

⨝ Condensed bowtie symbol (relation). Not available in Plain TeX.

Dotless j; used when you are putting an accent on a j (see Math accents ).

κ Lowercase Greek letter (ordinary).

Λ uppercase Greek letter (ordinary).

λ Lowercase Greek letter (ordinary).

∧ Logical and (binary). Synonym:  \wedge . See also logical or  \lor .

⟨ Left angle, or sequence, bracket (opening). Similar: less-than  < . Matches  \rangle .

{ Left curly brace (opening). Synonym:  \{ . Matches  \rbrace .

[ Left square bracket (opening). Synonym:  [ . Matches  \rbrack .

⌈ Left ceiling bracket, like a square bracket but with the bottom shaved off (opening). Matches  \rceil .

≤ Less than or equal to (relation). This is a synonym for  \leq .

⇝ Squiggly right arrow (relation). To get this symbol outside of math mode you can put \newcommand*{\Leadsto}{\ensuremath{\leadsto}} in the preamble and then use \Leadsto instead.

⇐ Is implied by, double-line left arrow (relation). Similar: single-line left arrow  \leftarrow .

← Single-line left arrow (relation). Synonym:  \gets . Similar: double-line left arrow  \Leftarrow .

↽ Single-line left harpoon, barb under bar (relation).

↼ Single-line left harpoon, barb over bar (relation).

⇔ Bi-implication; double-line double-headed arrow (relation). Similar: single-line double headed arrow  \leftrightarrow .

↔ Single-line double-headed arrow (relation). Similar: double-line double headed arrow  \Leftrightarrow .

≤ Less than or equal to (relation). This is a synonym for  \le .

⌊ Left floor bracket (opening). Matches:  \floor .

◁ Arrowhead, that is, triangle, pointing left (binary). For the normal subgroup symbol you should load amssymb and use  \vartriangleleft (which is a relation and so gives better spacing).

≪ Much less than (relation). Similar: much greater than  \gg .

¬ Logical negation (ordinary). Synonym:  \neg .

⟵ Long single-line left arrow (relation). Similar: long double-line left arrow  \Longleftarrow .

⟷ Long single-line double-headed arrow (relation). Similar: long double-line double-headed arrow  \Longleftrightarrow .

⟼ Long single-line left arrow starting with vertical bar (relation). Similar: shorter version  \mapsto .

⟶ Long single-line right arrow (relation). Similar: long double-line right arrow  \Longrightarrow .

∨ Logical or (binary). Synonym:  \vee . See also logical and  \land .

↦ Single-line left arrow starting with vertical bar (relation). Similar: longer version  \longmapsto .

℧ Conductance, half-circle rotated capital omega (ordinary).

∣ Single-line vertical bar (relation). A typical use of \mid is for a set \{\, x \mid x\geq 5 \,\} .

Similar: \vert and  | produce the same single-line vertical bar symbol but without any spacing (they fall in class ordinary) and you should not use them as relations but instead only as ordinals, i.e., footnote symbols. For absolute value, see the entry for  \vert and for norm see the entry for  \Vert .

⊨ Entails, or satisfies; double turnstile, short double dash (relation). Similar: long double dash  \vDash .

∓ Minus or plus (relation).

μ Lowercase Greek letter (ordinary).

∇ Hamilton’s del, or differential, operator (ordinary).

♮ Musical natural notation (ordinary).

≠ Not equal (relation). Synonym:  \neq .

↗ North-east arrow (relation).

¬ Logical negation (ordinary). Synonym:  \lnot . Sometimes instead used for negation:  \sim .

≠ Not equal (relation). Synonym:  \ne .

∋ Reflected membership epsilon; has the member (relation). Synonym:  \owns . Similar: is a member of  \in .

    Long solidus, or slash, used to overstrike a following operator (relation).

Many negated operators are available that don’t require \not , particularly with the amssymb package. For example, \notin is typographically preferable to \not\in .

∉ Not an element of (relation). Similar: not subset of  \nsubseteq .

ν Lowercase Greek letter (ordinary).

↖ North-west arrow (relation).

⊙ Dot inside a circle (binary). Similar: variable-sized operator  \bigodot .

∮ Contour integral, integral with circle in the middle (operator).

Ω uppercase Greek letter (ordinary).

ω Lowercase Greek letter (ordinary).

⊖ Minus sign, or dash, inside a circle (binary).

⊕ Plus sign inside a circle (binary). Similar: variable-sized operator  \bigoplus .

⊘ Solidus, or slash, inside a circle (binary).

⊗ Times sign, or cross, inside a circle (binary). Similar: variable-sized operator  \bigotimes .

∋ Reflected membership epsilon; has the member (relation). Synonym:  \ni . Similar: is a member of  \in .

∥ Parallel (relation). Synonym:  \| .

∂ Partial differential (ordinary).

⟂ Perpendicular (relation). Similar:  \bot uses the same glyph but the spacing is different because it is in the class ordinary.

Φ Uppercase Greek letter (ordinary).

ϕ Lowercase Greek letter (ordinary). The variant form is \varphi  φ.

Π uppercase Greek letter (ordinary).

π Lowercase Greek letter (ordinary). The variant form is \varpi  ϖ.

± Plus or minus (binary).

≺ Precedes (relation). Similar: less than  < .

⪯ Precedes or equals (relation). Similar: less than or equals  \leq .

′ Prime, or minute in a time expression (ordinary). Typically used as a superscript: $f^\prime$ ; $f^\prime$ and $f'$ produce the same result. An advantage of the second is that $f'''$ produces the desired symbol, that is, the same result as $f^{\prime\prime\prime}$ , but uses rather less typing. You can only use \prime in math mode. Using the right single quote  ' in text mode produces a different character (apostrophe).

∏ Product (operator).

∝ Is proportional to (relation)

Ψ uppercase Greek letter (ordinary).

ψ Lowercase Greek letter (ordinary).

⟩ Right angle, or sequence, bracket (closing). Similar: greater than  > . Matches: \langle .

} Right curly brace (closing). Synonym:  \} . Matches  \lbrace .

] Right square bracket (closing). Synonym:  ] . Matches  \lbrack .

⌉ Right ceiling bracket (closing). Matches  \lceil .

ℜ Real part, real numbers, cursive capital R (ordinary). Related: double-line, or blackboard bold, R  \mathbb{R} ; to access this, load the amsfonts package.

↾, Restriction of a function (relation). Synonym: \upharpoonright . Not available in plain TeX. In LaTeX you need to load the amssymb package.

⦰, Reversed empty set symbol (ordinary). Related: \varnothing . Not available in plain TeX. In LaTeX you need to load the stix package.

⌋ Right floor bracket, a right square bracket with the top cut off (closing). Matches  \lfloor .

◁ Arrowhead, that is, triangle, pointing right (binary). For the normal subgroup symbol you should instead load amssymb and use  \vartriangleright (which is a relation and so gives better spacing).

ρ Lowercase Greek letter (ordinary). The variant form is \varrho  ϱ.

⇒ Implies, right-pointing double line arrow (relation). Similar: right single-line arrow  \rightarrow .

→ Right-pointing single line arrow (relation). Synonym:  \to . Similar: right double line arrow  \Rightarrow .

⇁ Right-pointing harpoon with barb below the line (relation).

⇀ Right-pointing harpoon with barb above the line (relation).

⇌ Right harpoon up above left harpoon down (relation).

↘ Arrow pointing southeast (relation).

⧵ Set difference, reverse solidus or reverse slash, like \ (binary). Similar: backslash  \backslash and also \textbackslash outside of math mode.

♯ Musical sharp (ordinary).

Σ uppercase Greek letter (ordinary).

σ Lowercase Greek letter (ordinary). The variant form is \varsigma  ς.

∼ Similar, in a relation (relation).

≃ Similar or equal to, in a relation (relation).

∫ Integral sign that does not change to a larger size in a display (operator).

⌣ Upward curving arc, smile (ordinary).

♠ Spade card suit (ordinary).

⊓ Square intersection symbol (binary). Similar: intersection  cap .

⊔ Square union symbol (binary). Similar: union  cup . Related: variable-sized operator  \bigsqcup .

⊏, Square subset symbol (relation). Similar: subset  \subset . Not available in plain TeX. In LaTeX you need to load the amssymb package.

⊑ Square subset or equal symbol (binary). Similar: subset or equal to  \subseteq .

⊐, Square superset symbol (relation). Similar: superset  \supset . Not available in plain TeX. In LaTeX you need to load the amssymb package.

⊒ Square superset or equal symbol (binary). Similar: superset or equal  \supseteq .

⋆ Five-pointed star, sometimes used as a general binary operation but sometimes reserved for cross-correlation (binary). Similar: the synonyms asterisk  * and \ast , which are six-pointed, and more often appear as a superscript or subscript, as with the Kleene star.

⊂ Subset (occasionally, is implied by) (relation).

⊆ Subset or equal to (relation).

≻ Comes after, succeeds (relation). Similar: is less than  > .

⪰ Succeeds or is equal to (relation). Similar: less than or equal to  \leq .

∑ Summation (operator). Similar: Greek capital sigma  \Sigma .

⊃ Superset (relation).

⊇ Superset or equal to (relation).

√ Radical symbol (ordinary). The LaTeX command \sqrt{...} typesets the square root of the argument, with a bar that extends to cover the argument.

↙ Southwest-pointing arrow (relation).

τ Lowercase Greek letter (ordinary).

θ Lowercase Greek letter (ordinary). The variant form is \vartheta  ϑ.

× Primary school multiplication sign (binary). See also  \cdot .

→ Right-pointing single line arrow (relation). Synonym:  \rightarrow .

⊤ Top, greatest element of a partially ordered set (ordinary). See also  \bot .

△ Triangle (ordinary).

◁ Not-filled triangle pointing left (binary). Similar:  \lhd . For the normal subgroup symbol you should load amssymb and use  \vartriangleleft (which is a relation and so gives better spacing).

▷ Not-filled triangle pointing right (binary). For the normal subgroup symbol you should instead load amssymb and use  \vartriangleright (which is a relation and so gives better spacing).

⊴ Left-pointing not-filled underlined arrowhead, that is, triangle, with a line under (binary). For the normal subgroup symbol load amssymb and use  \vartrianglelefteq (which is a relation and so gives better spacing).

⊵ Right-pointing not-filled underlined arrowhead, that is, triangle, with a line under (binary). For the normal subgroup symbol load amssymb and use  \vartrianglerighteq (which is a relation and so gives better spacing).

⇑ Double-line upward-pointing arrow (relation). Similar: single-line up-pointing arrow  \uparrow .

↑ Single-line upward-pointing arrow, diverges (relation). Similar: double-line up-pointing arrow  \Uparrow .

⇕ Double-line upward-and-downward-pointing arrow (relation). Similar: single-line upward-and-downward-pointing arrow  \updownarrow .

↕ Single-line upward-and-downward-pointing arrow (relation). Similar: double-line upward-and-downward-pointing arrow  \Updownarrow .

↾, Up harpoon, with barb on right side (relation). Synonym:  \restriction . Not available in plain TeX. In LaTeX you need to load the amssymb package.

⊎ Multiset union, a union symbol with a plus symbol in the middle (binary). Similar: union  \cup . Related: variable-sized operator  \biguplus .

Υ uppercase Greek letter (ordinary).

υ Lowercase Greek letter (ordinary).

ε Small letter script epsilon (ordinary). This is more widely used in mathematics than the non-variant lunate epsilon form \epsilon  ϵ. Related: set membership  \in .

∅, Empty set symbol. Similar: \emptyset . Related: \revemptyset . Not available in plain TeX. In LaTeX you need to load the amssymb package.

φ Variant on the lowercase Greek letter (ordinary). The non-variant form is \phi  ϕ.

ϖ Variant on the lowercase Greek letter (ordinary). The non-variant form is \pi  π.

ϱ Variant on the lowercase Greek letter (ordinary). The non-variant form is \rho  ρ.

ς Variant on the lowercase Greek letter (ordinary). The non-variant form is \sigma  σ.

ϑ Variant on the lowercase Greek letter (ordinary). The non-variant form is \theta  θ.

⊢ Provable; turnstile, vertical and a dash (relation). Similar: turnstile rotated a half-circle  \dashv .

∨ Logical or; a downwards v shape (binary). Related: logical and  \wedge . Similar: variable-sized operator  \bigvee .

‖ Vertical double bar (ordinary). See Delimiters , for how to use the mathtools package to create flexibly-sized norm symbols.

| Single line vertical bar (ordinary). For “such that”, as in the definition of a set, use  \mid because it is a relation. See Delimiters , for how to use the mathtools package to create flexibly-sized absolute-value symbols.

∧ Logical and (binary). Synonym:  \land . See also logical or \vee . Similar: variable-sized operator  \bigwedge .

℘ Weierstrass p (ordinary).

≀ Wreath product (binary).

Ξ uppercase Greek letter (ordinary).

ξ Lowercase Greek letter (ordinary).

ζ Lowercase Greek letter (ordinary).

The following symbols are most often used in plain text but LaTeX provides versions to use in mathematical text.

Dollar sign in math mode: $.

Paragraph sign (pilcrow) in math mode, ¶.

Section sign in math mode: §.

Sterling sign in math mode: £.

Underscore in math mode: _.

  • \boldmath & \unboldmath
  • Blackboard bold
  • Calligraphic
  • Dots, horizontal or vertical
  • Greek letters

The LaTeX Network

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An Overleaf extension for recognizing symbols

Defining operators.

As we know, LaTeX has many commands to typeset operators , which are traditionally typeset using upright font—for example, sin, log etc. Obviously, the catalog of LaTeX’s operators is far from complete, especially because new ones are being constantly introduced. The question arises: what to do when we need a custom operator?

Probably one of the most often mistakes is to write something like

or, even worse,

sgn-bad

So what is the “right” way? As usually, there is more than one; but the simplest and cleanest one is to use the amsmath package:

(this is not necessary if you use one of the amsart, amsbook or amsrep classes) and then say

But there is one caveat. Some time ago I saw in my friend’s file the following code:

The result is disastrous: the space vanishes again! The explanation lies in the fact that TeX’s math mode treats everything in curly braces as an ordinary symbol, and we need an operator and not an ordinary symbol. The right way would be to define

—i.e., this would be the right way if there were no special command for that in the amsmath package. If you use some operator more often, it’s best to define it using the following construct:

where the first argument is the command and the second one the name to be typeset.

Again, there is a bit more to say. Assume that you want to have an operator like lim, which takes “limits” (in TeX’s terminology, this means that the sub- or superscript is to be placed below or above when in “displayed” mode). Then, you should use the starred version of \DeclareMathOperator:

ess sup

(This article is a rough translation of a Polish version, published on the author’s web site in 2008.)

Written by Marcin Borkowski

View all posts by Marcin Borkowski

This site is supported by donations to The OEIS Foundation .

List of LaTeX mathematical symbols

Pending changes are displayed on this page

All the predefined mathematical symbols from the T e X package are listed below. More symbols are available from extra packages.

  • 1 Greek letters
  • 2 Unary operators
  • 3 Relation operators
  • 4 Binary operators
  • 5 Negated binary relations
  • 6 Set and/or logic notation
  • 8 Delimiters
  • 10 Other symbols
  • 11 Trigonometric functions
  • 13 External links

Greek letters

Symbol LaTeX Symbol LaTeX
and and and and
and and and and
and and and and
and and , and , and
, and , and , and , and
and and , and , and
and and and and
, and , and and and
and and , , and , and
, and , and and and
and and and and
and and and and
Archaic Greek letters
Symbol LaTeX

Unary operators

Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment
 
                 

Relation operators

Symbol LaTeX Comment Symbol LaTeX Comment
is less than is greater than
is not less than is not greater than
is less than or equal to is greater than or equal to
is less than or equal to is greater than or equal to
is neither less than nor equal to is neither greater than nor equal to
is neither less than nor equal to is neither greater than nor equal to
precedes succeeds
doesn't precede doesn't succeed
precedes or equals succeeds or equals
neither precedes nor equals neither succeeds nor equals
   
   
is a proper subset of is a proper superset of
is not a proper subset of is not a proper superset of
is a subset of is a superset of
is not a subset of is not a superset of
   
   
Symbol LaTeX Comment
is equal to
 
is equivalent to
is approximately
is congruent to
is similar or equal to
is similar to
is proportional to
or or is not equal to
Symbol LaTeX Comment Symbol LaTeX Comment
is parallel with is not parallel with
is asymptotic to  
   
is member of owns, has member
   
models is not member of
is perpendicular with divides

Binary operators

Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment
plus or minus    
minus or plus    
multiplied by    
divided by      
asterisk      
       
     
       

Negated binary relations

Symbol LaTeX Comment Symbol LaTeX Comment
or or is not equal to is not member of
is not less than is not greater than
is not less than or equal to is not greater than or equal to
   
   
   
   
   
   
   
does not precede does not succeed
neither precedes nor equals neither succedes nor equals
   
   
   
is not similar to is not congruent to
   
  is not parallel with
   
   
   
   
   
   
   
   
   
   

Set and/or logic notation

Symbol LaTeX Comment
or , and or , and the
set of
set of
set of
set of
set of
set of
set of
set of
set of
is member of
is not member of
owns (has member)
is proper subset of
is subset of
is proper superset of
is superset of
Symbol LaTeX Comment
there is no
( )
( )
( )
or or
is implied by (only if)
is equivalent to (if and only if, iff)
 
 
Symbol LaTeX Comment Symbol LaTeX Comment
segment ray (half-line)
angle measured angle
triangle square
congruent (same shape and size) not congruent
similar (same shape) not similar
is parallel with is not parallel with
is perpendicular to is not perpendicular to
Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment
, is parallel with slash  
left parenthesis right parenthesis left [square] bracket right [square] bracket
left brace right brace left angle bracket right angle bracket
(left) (right) (left) (right)
       
Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment
or or        
       
or or        
Symbol LaTeX Comment Symbol LaTeX Comment
 
   
   

Other symbols

Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment Symbol LaTeX Comment
  ( )
     
  [Weierstrass]
Symbol LaTeX Comment
 
 

Trigonometric functions


arc is the abbreviation for arcus
Symbol LaTeX Symbol LaTeX Symbol LaTeX Symbol LaTeX

arcsinh arccosh (area hyperbolic functions), even though they are misnomers, since the prefix arc arcus ar area
Symbol LaTeX Symbol LaTeX Symbol LaTeX Symbol LaTeX

Sections remaining to be done : Table 3 onwards from symbols.pdf   (To do)   [1]

External links

  • Scott Pakin, The Comprehensive L a T e X Symbol List , 2017. (Lists thousands of symbols and the corresponding L a T e X commands that produce them.)
  • Comprehensive T e X Archive Network
  • http://ctan.cms.math.ca/tex-archive/info/symbols/comprehensive/SYMLIST
  • Mathematical symbols

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Equality and Inference Symbols in LaTeX

LaTeX is a typesetting system widely used for mathematical and scientific documents. One of its strengths is the ability to render complex mathematical symbols and notations effortlessly. This article focuses on the equality and inference symbols in LaTeX, providing a comprehensive guide on how to use them effectively.

Equality and Inference symbols are used to denote some relation between two physical quantities, numbers, sets, figures, or any two things. For example, we use = when two things are equal else we use ≠ . We cannot use our keyboard to write these symbols directly as these are not present on our keyboard. So we need LATex code to write them. Include \usepackage{amssymb} to use this notation. 

Table of Content

Equality and Inference Symbols and their LaTex Code

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TERMSYMBOLLATEX
Not equal to[Tex]\neq[/Tex]\neq
Similar to[Tex]\sim[/Tex]\sim
Dot equivalent[Tex]\doteq[/Tex]\doteq
Triangle Equivalent[Tex]\triangleq[/Tex]\triangleq
Thick similar to[Tex]\thicksim[/Tex]\thicksim
Divide[Tex]\div[/Tex]\div
Equivalent[Tex]\equiv[/Tex]\equiv
Dot equivalent[Tex]\doteq[/Tex]\doteq
Circle equivalent[Tex]\circeq[/Tex]\circeq
Not similar to[Tex]\nsim[/Tex]\nsim
Equality with a circle in between[Tex]\eqcirc[/Tex]\eqcirc
Thick approximate[Tex]\thickapprox[/Tex]\thickapprox
Falling Dots Equivalent[Tex]\fallingdotseq[/Tex]\fallingdotseq
Similar equal to[Tex]\simeq[/Tex]\simeq
Bump Equivalent[Tex]\bumpeq[/Tex]\bumpeq
Approximate[Tex]\approx[/Tex]\approx
Rising Dots Equivalent[Tex]\risingdotseq[/Tex]\risingdotseq
Double Bump Equivalent[Tex]\Bumpeq[/Tex]\Bumpeq
Approximately equal to[Tex]\approxeq[/Tex]\approxeq
Asymptotic[Tex]\asymp[/Tex]\asymp
Mid[Tex]\mid[/Tex]\mid
Parallel[Tex]\parallel[/Tex]\parallel
Not mid[Tex]\nmid[/Tex]\nmid
Not parallel to[Tex]\nparallel[/Tex]\nparallel
Short mid[Tex]\shortmid[/Tex]\shortmid
Short parallel to[Tex]\shortparallel[/Tex]\shortparallel
short not mid[Tex]\nshortmid[/Tex]\nshortmid
Short not parallel to[Tex]\nshortparallel[/Tex]\nshortparallel
Models[Tex]\models[/Tex]\models
Congruent to[Tex]\cong[/Tex]\cong
Not Congruent to[Tex]\ncong[/Tex]\ncong

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Logic Notations in LaTeX Maths Commands in LaTeX

1. Circuit Design

In electrical engineering, equality symbols are used to represent equations that describe circuit behaviors. Inference symbols help in logical reasoning for circuit analysis.

2. Control Systems

Equality and inference symbols are crucial in control systems engineering for formulating system equations and logical conditions for system stability and performance.

3. Structural Analysis

Structural engineers use equality symbols to denote equilibrium equations, while inference symbols are used in logical reasoning about load distribution and structural integrity.

Mastering the use of equality and inference symbols in LaTeX is essential for writing clear and accurate mathematical and scientific documents. These symbols play a vital role in various engineering fields, aiding in the representation of equations and logical reasoning. By using the commands and examples provided in this article, you can effectively incorporate these symbols into your LaTeX documents.

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Assignments

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Bitwise operator in pseudo-code

I am translating a C++ program into pseudo-code using the algorithmicx package.

Do you know how I can represent the C bitwise operator like the shifts (<< and >>) ?

Until now I used power of 2 but it's not very convenient.

Martin Scharrer's user avatar

  • Can you please explain what you mean by "I used power of 2"? –  Hendrik Vogt Commented Mar 25, 2011 at 11:04
  • @Hendrik: Apparently x \cdot 2^n and x / 2^n , where n is the shift amount. –  Andrey Vihrov Commented Mar 25, 2011 at 11:08
  • @Andrey: Thanks, now I get it - in pseudo-code that's not too bad. –  Hendrik Vogt Commented Mar 25, 2011 at 11:26
  • @HendrikVogt: Notice that << behaves differently than power when running out of bits. –  user877329 Commented Feb 16, 2015 at 12:18

5 Answers 5

Pseudocode has a different purpose compared to the actual programs. It should convey ideas, not implementation, and as such should be as close to the natural language as possible. Therefore I think it's not good to introduce programming language-specific syntax in the algorithm listing.

I suggest one of these options:

  • continue using algorithmicx and select a human-readable name for the operation: \State $x \gets \Call{ShiftLeft}{x, 3}$ ;
  • use the listings package and typeset the actual C++ program with comments.

Andrey Vihrov's user avatar

  • Ok I will use the Call (I didn't know it). –  BenjaminB Commented Mar 25, 2011 at 11:45

I advise against Andrey’s solution. He is right that in general pseudocode should be independent of a specific machine or language.

But this breaks down with bit operations. Bit operations do suggest a specific underlying architecture, and the bit operators follow an established nomenclature.

You don’t make the code more readable by ignoring this convention – in fact, you do the opposite.

I have the following commands defined in my thesis template:

(The command names follow the naming convention of the algorithmicx package which I can recommend for typesetting algorithms.)

That said, you should second-guess your reason for using bit operations in the first place – often they are only used to achieve specific optimisations, in which case they have no place in a pseudo-code. On the other hand, sometimes (and it sounds as if this may be the case for you) they have a legitimate purpose.

Konrad Rudolph's user avatar

  • 1 I agree that your point is valid. A yet better approach would be to use the C-style notation and add a list of operators and their meanings somewhere in the beginning of the document. This eliminates any possible confusion. –  Andrey Vihrov Commented Jul 23, 2011 at 9:32
  • How about \BitXor ? I tried \newcommand{\BitXor}{\mathrel{\^}} and it's giving me problems (in MathJax, maybe something strange there, but the other commands worked (non-starred) ) –  Nick T Commented Nov 24, 2015 at 15:43
  • @NickT See tex.stackexchange.com/q/77646/42 . –  Konrad Rudolph Commented Nov 24, 2015 at 16:24
  • 1 It seems \mathbin is more appropriate than \mathrel . –  xskxzr Commented Apr 14, 2019 at 11:27

For symbols, you can use \ll and \gg for shifting, and \lll , \ggg for rotating.

enter image description here

You can also define some functions:

and use $\shl(a,n)$ etc. in the algorithm.

Leo Liu's user avatar

  • \ll and \gg means more "very lower" and "very greater" rather than bit level shift. –  BenjaminB Commented Mar 25, 2011 at 11:06
  • @Ubiquité: Yes, I know that. But they are actully used in some algorithm descriptions, especially in figures. For example, en.wikipedia.org/wiki/SHA-1 –  Leo Liu Commented Mar 25, 2011 at 11:17
  • Plus, in the 'normal' representation of the programming construct, they are not, I think, kerned. –  Brent.Longborough Commented Mar 25, 2011 at 13:34
  • @Brent But they look better when kerned. Pretty-printed pseudo-code can take some freedom with operators. Many authors do this and in some cases (Haskell and ML come to mind) this is actually encouraged and something of a standard. –  Konrad Rudolph Commented Mar 25, 2011 at 15:10
  • @Konrad: Knuth's WEB comes to mind too. weave tex.web and then run pdftex tex . –  TH. Commented Mar 25, 2011 at 20:31

Use the \verb command, e. g.

if you need to have those operators displayed exactly as they would be typed in a program, and do not want to use other packages for that.

PointedEars's user avatar

In mathematics \ll is often used for "much less than" and using both in one document creates a need to distinguish this symbol from the bit shift operator.

My suggestion is to combine the answers of Konrad and PointedEars thusly:

The \verb command is overpowered for this purpose and has some restrictions which make it harder to work with. I use \texttt{<<} instead, as it may more easily be included into macros. It's also a good idea to make a macro out of whatever you settle on, so in the future you only have to change it in one place if you change your mind.

Werner's user avatar

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COMMENTS

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    Just put this code into your preamble. Then you can use := as usual, and you'll get horizontal symmetry. Much easier to use than \coloneqq, in my opinion. Per @Will Robertson's comment, there is also a feature of mathtools to change the vertical alignment of all colons in math mode. \mathtoolsset{centercolon}

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  13. PDF The Comprehensive LaTeX Symbol List

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  21. LaTeX Templates

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  22. Bitwise operator in pseudo-code

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  23. Gallery

    Here we provide a selection of homework assignments templates and examples for school, college and university use. These often include a question and answer section already set out, along with space for the student name, course title, date and any other required information. Teachers and lecturers may also find these templates useful for ...