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Essential LaTeX: A Comprehensive Guide to Mathematical Symbols and Relations, Study notes of Number Theory

An essential reference for LaTeX users, featuring tables of mathematical symbols and relations, including Greek letters, binary operation symbols, delimiters, and miscellaneous symbols. It also includes examples of how to use these symbols in mathematical equations.

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

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20 ESS ENT IAL L
ATEX
A Mathematical symbols
\alpha
\beta
\gamma
\delta
\epsilon
\varepsilon
\zeta
\eta
\theta
\vartheta
\iota
\kappa
\lambda
\mu
\nu
\xi
o
\pi
\varpi
\rho
\varrho
\sigma
\varsigma
\tau
\upsilon
\phi
\varphi
\chi
\psi
\omega
\Gamma
\Delta
\Theta
!
\Lambda
"
\Xi
#
\Pi
$
\Sigma
%
\Upsilon
&
\Phi
'
\Psi
(
\Omega
Table 1: Greek letters
)
\pm
*
\cap
+
\diamond
,
\oplus
-
\mp
.
\cup
/
\bigtriangleup
0
\ominus
1
\times
2
\uplus
3
\bigtriangledown
4
\otimes
5
\div
6
\sqcap
7
\triangleleft
8
\oslash
9
\ast
:
\sqcup
;
\triangleright
<
\odot
=
\star
>
\vee
?
\lhd
@ A
\bigcirc
B
\circ
C
\wedge
D
\rhd
@ E
\dagger
F
\bullet
G
\setminus
H
\unlhd
@ I
\ddagger
J
\cdot
K
\wr
L
\unrhd
@ M
\amalg
@
Not predefined in L
A
TEX2
N
. Use the packages latexsym or amssymb
Table 2: Binary operation symbols
O
\leq
P
\geq
Q
\equiv
RS
\models
T
\prec
U
\succ
V
\sim
W
\perp
X
\preceq
Y
\succeq
Z
\simeq
R
\mid
[
\ll
\
\gg
]
\asymp
^
\parallel
_
\subset
`
\supset
a
\approx
;b7
\bowtie
c
\subseteq
d
\supseteq
V
S
\cong
e
\Join
f
\sqsubset
g
\sqsupset
hS
\neq
i
\smile
j
\sqsubseteq
k
\sqsupseteq
l
S
\doteq
m
\frown
n
\in
o
\ni
p
\propto
S
=
q
\vdash
r
\dashv
s
<
t
>
Table 3: Relation symbols
pf3
pf4
pf5

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A Mathematical symbols

\alpha  \beta  \gamma  \delta  \epsilon  \varepsilon  \zeta  \eta  \theta \vartheta \iota \kappa \lambda \mu  \nu  \xi  o  \pi  \varpi  \rho  \varrho  \sigma  \varsigma  \tau  \upsilon  \phi  \varphi  \chi  \psi  \omega  "^ \Gamma^  \Delta^ \Theta^! \Lambda &^ \Xi^ # \Pi^ $ \Sigma^ % \Upsilon \Phi ' \Psi ( \Omega

Table 1: Greek letters

) \pm * \cap + \diamond , \oplus

  • \mp. \cup / \bigtriangleup 0 \ominus (^1) \times 2 \uplus 3 \bigtriangledown 4 \otimes (^5) \div 6 \sqcap 7 \triangleleft 8 \oslash (^9) \ast : \sqcup ; \triangleright < \odot = \star > \vee? \lhd @ A \bigcirc B \circ C \wedge D \rhd @ E \dagger F \bullet G \setminus H \unlhd @ I \ddagger J \cdot K \wr L \unrhd @ M \amalg @ Not predefined in LATEX 2N. Use the packages latexsym or amssymb

Table 2: Binary operation symbols

O \leq P \geq Q \equiv RS \models T \prec U \succ V \sim W \perp X \preceq Y \succeq Z \simeq R \mid [ \ll \ \gg ] \asymp ^ c^ \parallel^ _ \subset^ ` \supset^ a \approx^ ;b7^ \bowtie \subseteq d \supseteq VS \cong e \Join f \sqsubset g l^ \sqsupset^ Sh \neq^ i \smile^ j \sqsubseteq^ k \sqsupseteq S \doteq m \frown n \in o \ni p \propto S = q \vdash r \dashv s < t >

Table 3: Relation symbols

 \rmoustache

  \lmoustache

 \rgroup

  \lgroup   \arrowvert   \Arrowvert   

\bracevert

Table 4: Large delimiters

 \uparrow  \Uparrow \downarrow \Downarrow ^ {^ }^ \updownarrow^  \Updownarrow  \lfloor^  \rfloor^  \lceil^  \rceil \langle  \rangle  / G \backslash R |

^ |

Table 5: Delimiters

 \leftarrow  (^) \longleftarrow  \uparrow  \Leftarrow  S \Longleftarrow  \Uparrow  \rightarrow  (^) \longrightarrow \downarrow  \Rightarrow S  \Longrightarrow \Downarrow  \leftrightarrow   \longleftrightarrow \updownarrow  \Leftrightarrow   \Longleftrightarrow  \Updownarrow ! \mapsto !^ \longmapsto " \nearrow $# \hookleftarrow %  \hookrightarrow & \searrow ' \leftharpoonup ( \rightharpoonup ) \swarrow

  • \leftharpoondown + \rightharpoondown , \nwarrow

Table 6: Arrow symbols

lll \ldots JJJ \cdots

. \vdots

. (^) \ddots - \aleph . 3 \prime^ / \forall^0 \infty^1 \hbar^2 \emptyset 7 \exists^4 \nabla^5 \surd^6 \Box@^ / \triangle = \Diamond@^98 \imath^ : \jmath^ ; \ell^ < \neg \top > \flat? \natural @ \sharp A \wp

F^ W^ \bot^ B \clubsuit^ C \diamondsuit^ D \heartsuit^ E \spadesuit \mho@ G \Re H \Im I \angle J \partial @ Not predefined in LATEX 2N. Use the packages latexsym or amssymb

Table 7: Miscellaneous symbols

\digamma  \varkappa  \beth  \daleth  \gimel

Table 13: AMS Greek and Hebrew

 \ulcorner  \urcorner  \llcorner  \lrcorner

Table 14: AMS delimiters

^ \dashrightarrow^ ^ \dashleftarrow^  \leftleftarrows \leftrightarrows  \Lleftarrow  \twoheadleftarrow  \leftarrowtail  \looparrowleft  \leftrightharpoons  \curvearrowleft  \circlearrowleft  \Lsh  \upuparrows  \upharpoonleft  \downharpoonleft  \multimap  \leftrightsquigarrow  \rightrightarrows  \rightleftarrows  \rightrightarrows

 \rightleftarrows \twoheadrightarrow! \rightarrowtail " \looparrowright

\rightleftharpoons $ \curvearrowright % \circlearrowright

& )^ \Rsh^ ' \downdownarrows^ ( \upharpoonright \downharpoonright * \rightsquigarrow

Table 15: AMS arrows

  • \nleftarrow , \nrightarrow - \nLeftarrow . \nRightarrow / \nleftrightarrow 0 \nLeftrightarrow

Table 16: AMS negated arrows

1 \dotplus 2 \smallsetminus 3 \Cap 4 7 \Cup^5 \barwedge^6 \veebar \doublebarwedge 8 \boxminus 9 \boxtimes : \boxdot ; \boxplus < \divideontimes = \ltimes > \rtimes? \leftthreetimes @ \rightthreetimes A \curlywedge B \curlyvee C \circleddash D \circledast E \circledcirc F \centerdot G \intercal

Table 17: AMS binary operators

^ \leqq^  \leqslant^  \eqslantless \lesssim  \lessapprox  \approxeq  \lessdot  \lll  \lessgtr

\lesseqgtr \lesseqqgtr \doteqdot \risingdotseq \fallingdotseq  \backsim  \backsimeq  \subseteqq  \Subset f \sqsubset  \preccurlyeq  \curlyeqprec  \precsim^  \precapprox^  \vartriangleleft \trianglelefteq  \vDash  \Vvdash  \smallsmile  \smallfrown  \bumpeq  \Bumpeq  \geqq  \geqslant \eqslantgtr! \gtrsim " \gtrapprox

\gtrdot $ \ggg % \gtrless

& \gtreqless ' \gtreqqless ( \eqcirc ) \circeq * \triangleq + \thicksim , \thickapprox - \supseteqq. \Supset g 1 \sqsupset^ / \succcurlyeq^0 \curlyeqsucc \succsim 2 \succapprox 3 \vartriangleright 4 \trianglerighteq 5 \Vdash 6 \shortmid (^7) \shortparallel 8 \between 9 \pitchfork : \varpropto ; \blacktriangleleft < \therefore = \backepsilon > \blacktriangleright? \because

Table 18: AMS binary relations

@ C^ \nless^ A \nleq^ B \nleqslant F \nleqq^ D \lneq^ E \lneqq I \lvertneqq^ G \lnsim^ H \lnapprox L \nprec^ J \npreceq^ K \precnsim O \precnapprox^ M \nsim^ N \nshortmid R \nmid^ P \nvdash^ Q \nvDash \ntriangleleft S \ntrianglelefteq T \nsubseteq U X \subsetneq^ V \varsubsetneq^ W \subsetneqq [ \varsubsetneqq^ Y \ngtr^ Z \ngeq ^ \ngeqslant^ \ \ngeqq^ ] \gneq a \gneqq^ _ \gvertneqq^ ` \gnsim d \gnapprox^ b \nsucc^ c \nsucceq \succnsim e \succnapprox f \ncong g \nshortparallel h \nparallel Q \nvDash i l \nVDash^ j \ntriangleright^ k \ntrianglerighteq \nsupseteq m \nsupseteqq n \supsetneq o \varsupsetneq p \supsetneqq q \varsupsetneqq

Table 19: AMS negated binary relations

) i i i i i i

 6    a 6  a! 6  !

 D^6 :^6

 D  : 

i i i i i i

i

i

i

i

 D^6

 D  i

i

i

i

 Z i i i i

D^6 :^6

:^6

i

i

i

i

 Z i i i i

D  : 

i

i

i

i

\begin{displaymath} \frac{\pm \left|\begin{array}{ccc} x_1-x_2 & y_1-y_2 & z_1-z_2 \ l_1 & m_1 & n_1 \ l_2 & m_2 & n_ \end{array}\right|}{ \sqrt{\left|\begin{array}{cc}l_1&m_1\ l_2&m_2\end{array}\right|ˆ

  • \left|\begin{array}{cc}m_1&n_1\ n_1&l_1\end{array}\right|ˆ
  • \left|\begin{array}{cc}m_2&n_2\ n_2&l_2\end{array}\right|ˆ2}} \end{displaymath}

   L^ L

 L

 S 



 ^1 @@A

&

 ^

^ ^

  Z       

Z  

Z

^ ^

  Z    



Z



G

G

I

\newcommand{\CA}{C_{\rm A}} \newcommand{\CV}{C_{\rm V}} \newcommand{\CPA}{{C’}{\rm A}} \newcommand{\CPV}{{C’}{\rm V}} \newcommand{\GZ}{\Gammaˆ2_{\rm Z}} \newcommand{\MZ}{Mˆ2_{\rm Z}} \newcommand{\MZs}{{(s-Mˆ2_{\rm Z})}} \newcommand{\BE}{\left{\frac{\displaystyle 3-\betaˆ2}{\displaystyle 2}\right}} \begin{eqnarray} \sigmaˆf_0(Q,T_{3R},\beta,s) & = & \frac{4\pi\alphaˆ2}{3s}\beta \times \left[ \frac{Qˆ2 \BE - 2Q \CV \CPV s \MZs}{\MZsˆ2 + \MZ \GZ \BE} \right. \nonumber \[-3mm] & & \[-3mm] & + & \left.\frac{(\CVˆ2 + \CAˆ2) sˆ2}% {\MZsˆ2+\MZ\GZ\left{\CPVˆ2 \BE+\CPAˆ2 {\betaˆ2}\right}} \right] \nonumber \end{eqnarray}

Bibliography

1 Leslie Lamport. LATEX—A Document Preparation System—User’s Guide and Reference Manu- al. Addison-Wesley, Reading, MA, USA, 1985.

2 Donald E. Knuth. The TEXbook , volume A of Computers and Typesetting. Addison-Wesley, Reading, MA, USA, 1986.

3 Michel Goossens, Frank Mittelbach and Alexander Samarin. The LATEX Companion Addison- Wesley, Reading, MA, USA, 1993.