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lim
sup
lim inf
\liminf
lim
inf
curl
\text{curl}
curl
rot
\text{rot}
rot
inj lim
\text{inj~lim}
inj
lim
proj lim
\text{proj~lim}
proj
lim
div
\text{div}
div
OR
\text{OR}
OR
AND
\text{AND}
AND
XOR
\text{XOR}
XOR
NOR
\text{NOR}
NOR
NAND
\text{NAND}
NAND
XNOR
\text{XNOR}
XNOR
deg
\deg
de
g
Bin
\text{Bin}
Bin
Geo
\text{Geo}
Geo
min
\min
min
max
\max
max
1
2
\frac{1}{2}
2
1
3
4
\frac{\displaystyle{}3}{\displaystyle{}4}
4
3
1
2
+
3
4
+
5
6
\frac{\displaystyle{}1}{\displaystyle{}2}+\frac{\displaystyle{}3}{\displaystyle{}4}+\frac{\displaystyle{}5}{\displaystyle{}6}
2
1
+
4
3
+
6
5
88
19
+
27
73
\frac{{88}}{{19}} + \frac{{27}}{{73}}
19
88
+
73
27
1
2
\frac{\displaystyle{}1}{\displaystyle{}2}
2
1
1
2
\frac{1}{2}
2
1
1
2
\tfrac{1}{2}
2
1
1
1
+
1
2
\frac{1}{1+\frac{1}{2}}
1
+
2
1
1
1
1
+
1
2
\tfrac{1}{1+\frac{1}{2}}
1
+
2
1
1
1
2
\dfrac{1}{2}
2
1
1
1
+
1
2
\cfrac{1}{1 + \cfrac{1}{2}}
1
+
2
1
1
1
2
+
3
4
+
5
6
+
⋱
\frac{\displaystyle{}1}{\displaystyle{}2+\frac{\displaystyle{}3}{\displaystyle{}4+\frac{\displaystyle{}5}{\displaystyle{}6+⋱}}}
2
+
4
+
6
+
⋱
5
3
1
=
=
=
x
=
x=
x
=
x
=
y
=
2
x= y= 2
x
=
y
=
2
x
=
y
=
0
x = y = 0
x
=
y
=
0
x
=
1
=
2
\begin{aligned} & x\\ & = 1\\ & = 2 \end{aligned}
x
=
1
=
2
x
=
1
=
2
\begin{aligned} x & = 1\\ & = 2 \end{aligned}
x
=
1
=
2
x
=
1
=
2
\begin{aligned} & ~ \quad x\\ & = 1\\ & = 2 \end{aligned}
x
=
1
=
2
x
=
1
=
2
\begin{aligned}x & =1 \\ & =2 \end{aligned}
x
=
1
=
2
x
=
1
=
2
\begin{aligned} & ~ \quad x \\ & =1 \\ & =2 \end{aligned}
x
=
1
=
2
a
≡
b
(
m
o
d
2
)
a≡b\pmod 2
a
≡
b
(
mod
2
)
x
≡
y
≡
0
(
m
o
d
5
)
x ≡ y ≡ 0 \pmod {5}
x
≡
y
≡
0
(
mod
5
)
x
≡
1
≡
2
\begin{aligned}x & ≡1 \\ & ≡2 \end{aligned}
x
≡
1
≡
2
x
≡
1
≡
2
\begin{aligned} & ~ \quad x \\ & ≡1 \\ & ≡2 \end{aligned}
x
≡
1
≡
2
1
=
[
m
o
d
2
]
−
1
1\xlongequal{}[\mod 2]{}-1
1
[
mod
2
]
−
1
≤
≤
≤
x
≤
x≤
x
≤
x
=
y
≤
2
x= y≤ 2
x
=
y
≤
2
≥
≥
≥
x
=
y
≠
2
x= y≠ 2
x
=
y
=
2
≠
≠
=
a
̸
≡
b
(
m
o
d
2
)
a\not \mathrlap{} \negthickspace \negthickspace ≡b\pmod 2
a
≡
b
(
mod
2
)
x
1
2
{x}_1^2
x
1
2
x
2
{x}^2
x
2
x
3
{x}^3
x
3
x
−
1
{x}^{-1}
x
−
1
x
1
{x}_1
x
1
e
π
i
{e}^{πi}
e
πi
r
e
i
θ
{r}e^{iθ}
r
e
i
θ
e
i
π
2
{e}^{\frac{iπ}2}
e
2
iπ
C
n
m
C_{n}^{m}
C
n
m
2
1
\stackrel{1}{2}
2
1
2
1
\overset{1}{2}
2
1
1
2
\underset{2}{1}
2
1
1
2
1 \atop2
2
1
1
2
1 \above{}2
2
1
1
2
1 \above{1pt}2
2
1
1
2
1 \above{2pt}2
2
1
2
\sqrt{2}
2
3
3
\sqrt[3]{3}
3
3
4
4
\sqrt[4]{4}
4
4
a
b
\sqrt{{ab}}
ab
x
−
y
3
\sqrt{x-\sqrt[3]{y}}
x
−
3
y
x
\sqrt{x}
x
x
3
\sqrt[3]{x}
3
x
x
4
\sqrt[4]{x}
4
x
2
2
\frac{\displaystyle{}\sqrt{2}}{\displaystyle{}2}
2
2
5
−
1
2
\frac{\displaystyle{}\sqrt{5}-1}{\displaystyle{}2}
2
5
−
1
−
b
±
b
2
−
4
a
c
2
a
\frac{\displaystyle{}-b±\sqrt{b^2-4ac}}{\displaystyle{}2a}
2
a
−
b
±
b
2
−
4
a
c
1
+
10
+
100
+
1000
+
⋯
5
4
3
\sqrt{1+\sqrt[3]{10+\sqrt[4]{100+\sqrt[5]{1000+⋯}}}}
1
+
3
10
+
4
100
+
5
1000
+
⋯
d
f
d
x
\tfrac{\mathrm{d} f}{\mathrm{d} x}
d
x
d
f
d
f
d
x
\tfrac{\mathrm{d} f}{\mathrm{d} x}
d
x
d
f
∂
f
∂
x
\tfrac{∂ f}{∂ x}
∂
x
∂
f
d
d
x
\tfrac{\mathrm{d} }{\mathrm{d} x}
d
x
d
∂
∂
x
\tfrac{∂ }{∂ x}
∂
x
∂
d
x
\hskip{0.1em}\text{d}x
d
x
d
y
\mathrm{d}y
d
y
∂
x
∂x
∂
x
d
x
∧
d
y
\hskip{0.1em}\text{d}x∧\hskip{0.1em}\text{d}y
d
x
∧
d
y
∇
\nabla
∇
d
2
f
d
x
2
\tfrac{\mathrm{d} ^{2}f}{\mathrm{d} x^{2}}
d
x
2
d
2
f
∂
2
f
∂
x
2
\tfrac{∂ ^{2}f}{∂ x^{2}}
∂
x
2
∂
2
f
d
2
f
d
x
d
y
\tfrac{\mathrm{d} ^{2}f}{\mathrm{d} x\mathrm{d} y}
d
x
d
y
d
2
f
∂
2
f
∂
x
∂
y
\tfrac{∂ ^{2}f}{∂ x∂ y}
∂
x
∂
y
∂
2
f
∂
(
x
,
y
)
∂
(
u
,
v
)
\tfrac{∂ (x,y)}{∂ (u,v)}
∂
(
u
,
v
)
∂
(
x
,
y
)
∣
∂
(
x
,
y
)
∂
(
u
,
v
)
∣
\left| \tfrac{∂ (x,y)}{∂ (u,v)}\right|
∂
(
u
,
v
)
∂
(
x
,
y
)
∂
3
f
∂
x
∂
y
∂
z
\tfrac{∂ ^{3}f}{∂ x∂ y∂ z}
∂
x
∂
y
∂
z
∂
3
f
Σ
\Sigma
Σ
Π
\Pi
Π
∑
\sum
∑
∏
\prod
∏
∑
∑
∑
Σ
Σ
Σ
∑
i
=
0
∞
f
\displaystyle{\sum\limits_{i=0}^{∞}f}
i
=
0
∑
∞
f
⋃
i
=
0
∞
f
\displaystyle{\bigcup\limits_{i=0}^{∞}f}
i
=
0
⋃
∞
f
⋁
i
=
0
∞
f
\displaystyle{\bigvee\limits_{i=0}^{∞}f}
i
=
0
⋁
∞
f
⨁
i
=
0
∞
f
\displaystyle{\bigoplus\limits_{i=0}^{∞}f}
i
=
0
⨁
∞
f
∑
i
+
j
=
10
f
\displaystyle{\sum\limits_{i+j=10}f}
i
+
j
=
10
∑
f
∏
i
=
0
∞
f
\displaystyle{\prod\limits_{i=0}^{∞}f}
i
=
0
∏
∞
f
⋂
i
=
0
∞
f
\displaystyle{\bigcap\limits_{i=0}^{∞}f}
i
=
0
⋂
∞
f
⋀
i
=
0
∞
f
\displaystyle{\bigwedge\limits_{i=0}^{∞}f}
i
=
0
⋀
∞
f
⨂
i
=
0
∞
f
\displaystyle{\bigotimes\limits_{i=0}^{∞}f}
i
=
0
⨂
∞
f
∏
i
∣
24
f
\displaystyle{\prod\limits_{i|24}f}
i
∣24
∏
f
∐
i
=
0
∞
f
\displaystyle{\coprod\limits_{i=0}^{∞}f}
i
=
0
∐
∞
f
⨀
i
=
0
∞
f
\displaystyle{\bigodot\limits_{i=0}^{∞}f}
i
=
0
⨀
∞
f
∑
i
+
j
=
10
i
<
j
f
\displaystyle{\sum\limits_{\substack{i+j=10\\ i<j}}f}
i
+
j
=
10
i
<
j
∑
f
+
i
=
0
∞
f
\displaystyle{\mathop{+}\limits_{i=0}^{∞}f}
i
=
0
+
∞
f
sup
i
=
0
∞
f
\displaystyle{\sup\limits_{i=0}^{∞}f}
i
=
0
sup
∞
f
max
i
=
0
∞
f
\displaystyle{\max\limits_{i=0}^{∞}f}
i
=
0
max
∞
f
×
i
=
0
∞
f
\displaystyle{\mathop{×}\limits_{i=0}^{∞}f}
i
=
0
×
∞
f
inf
i
=
0
∞
f
\displaystyle{\inf\limits_{i=0}^{∞}f}
i
=
0
in
f
∞
f
min
i
=
0
∞
f
\displaystyle{\min\limits_{i=0}^{∞}f}
i
=
0
min
∞
f
∗
−
∞
∞
f
\mathop{*}\limits_{-∞}^{∞}f
−
∞
∗
∞
f
lim
\lim
lim
lim
x
→
+
∞
f
\lim\limits_{x \to +∞}f
x
→
+
∞
lim
f
lim
x
→
−
∞
f
\lim\limits_{x \to -∞}f
x
→
−
∞
lim
f
∞
\infty
∞
lim
x
→
0
f
\lim\limits_{x \to 0}f
x
→
0
lim
f
lim
x
→
0
+
f
\lim\limits_{x \to 0^+}f
x
→
0
+
lim
f
lim
‾
x
→
0
f
\underset{x \to 0}{\overline{\lim}}\,f
x
→
0
lim
f
lim
‾
x
→
0
f
\underset{x \to 0}{\underline{\lim}}\,f
x
→
0
lim
f
e
x
=
lim
n
→
∞
(
1
+
x
n
)
n
e^x=\lim\limits_{n \to ∞}\left( 1+\frac{\displaystyle{}x}{\displaystyle{}n}\right) ^{n}
e
x
=
n
→
∞
lim
(
1
+
n
x
)
n
lim
x
→
0
y
→
0
f
(
x
,
y
)
\lim\limits_{\substack{x→0\\y→0}}f(x,y)
x
→
0
y
→
0
lim
f
(
x
,
y
)
∫
\int
∫
∫
\smallint
∫
∫
\textstyle\int
∫
∫
L
\int \limits_{L}
L
∫
∫
L
d
s
\displaystyle{\int\limits_{L}\,\mathrm{d}{s}}
L
∫
d
s
F
(
x
)
∣
1
0
F(x)\LARGE|\normalsize\substack{1\\\\ 0}
F
(
x
)
∣
1
0
∫
−
1
1
f
d
x
\displaystyle{\int\nolimits_{-1}^{1}f\,\mathrm{d}{x}}
∫
−
1
1
f
d
x
∫
−
∞
+
∞
f
d
x
\displaystyle{\int\nolimits_{-∞}^{+∞}f\,\mathrm{d}{x}}
∫
−
∞
+
∞
f
d
x
∫
0
x
f
(
t
)
d
t
\displaystyle{\int\nolimits_{0}^{x}f(t)\,\mathrm{d}{t}}
∫
0
x
f
(
t
)
d
t
∣
2
π
0
\LARGE|\normalsize\substack{2π\\\\ 0}
∣
2
π
0
∫
L
P
d
x
+
Q
d
y
\displaystyle{\int\limits_{L}P\mathrm{d}{x}+Q\mathrm{d}{y}}
L
∫
P
d
x
+
Q
d
y
∫
∂
M
ω
=
∫
M
d
ω
\displaystyle{\int\limits_{∂M}ω\,}=\displaystyle{\int\limits_{M}\,\mathrm{d}{ω}}
∂
M
∫
ω
=
M
∫
d
ω
∫
0
2
π
d
θ
∫
0
1
f
d
ρ
\displaystyle{\int\nolimits_{0}^{2π}\,\mathrm{d}{θ}}\displaystyle{\int\nolimits_{0}^{1}f\,\mathrm{d}{ρ}}
∫
0
2
π
d
θ
∫
0
1
f
d
ρ
∮
L
P
d
x
+
Q
d
y
=
∬
D
(
∂
Q
∂
x
−
∂
P
∂
y
)
d
x
d
y
\displaystyle{\oint\limits_{L}P\mathrm{d}{x}+Q\mathrm{d}{y}}=\displaystyle{\iint\limits_{D}\left( \tfrac{∂ Q}{∂ x}- \tfrac{∂ P}{∂ y}\right) \,\mathrm{d}{x}\mathrm{d}{y}}
L
∮
P
d
x
+
Q
d
y
=
D
∬
(
∂
x
∂
Q
−
∂
y
∂
P
)
d
x
d
y
∫
0
1
d
x
∫
0
1
f
d
y
\displaystyle{\int\nolimits_{0}^{1}\,\mathrm{d}{x}}\displaystyle{\int\nolimits_{0}^{1}f\,\mathrm{d}{y}}
∫
0
1
d
x
∫
0
1
f
d
y
∬
Σ
f
d
σ
\displaystyle{\iint\limits_{Σ}f\,\mathrm{d}σ}
Σ
∬
f
d
σ
∬
Σ
f
d
x
d
y
\displaystyle{\iint\limits_{Σ}f\,\mathrm{d}{x}\mathrm{d}{y}}
Σ
∬
f
d
x
d
y
∬
Σ
f
d
φ
d
θ
\displaystyle{\iint\limits_{Σ}f\,\mathrm{d}{φ}\mathrm{d}{θ}}
Σ
∬
f
d
φ
d
θ
∬
x
2
+
y
2
=
1
x
≥
0
f
d
x
d
y
\displaystyle{\iint\limits_{\substack{x^2+y^2=1\\ x≥0}}f\,\mathrm{d}{x}\mathrm{d}{y}}
x
2
+
y
2
=
1
x
≥
0
∬
f
d
x
d
y
∯
Σ
P
d
x
d
y
+
Q
d
y
d
z
+
R
d
z
d
x
\displaystyle{\oiint\limits_{Σ}P\mathrm{d}{x\mathrm{d}y}+Q\mathrm{d}{y\mathrm{d}z}+R\mathrm{d}{z\mathrm{d}x}}
Σ
∬
P
d
x
d
y
+
Q
d
y
d
z
+
R
d
z
d
x
∬
Σ
f
d
x
∧
d
y
\displaystyle{\iint\limits_{Σ}f\,\mathrm{d}{x}∧\mathrm{d}{ y}}
Σ
∬
f
d
x
∧
d
y
∭
Ω
f
d
V
\displaystyle{\iiint\limits_{Ω}f\,\mathrm{d}V}
Ω
∭
f
d
V
∭
Ω
f
d
x
d
y
d
z
\displaystyle{\iiint\limits_{Ω}f\,\mathrm{d}{x}\mathrm{d}{y}\mathrm{d}{z}}
Ω
∭
f
d
x
d
y
d
z
∫
⋯
∫
−
∞
+
∞
f
d
x
\displaystyle{\int\dotsi\int\nolimits_{-∞}^{+∞}f\,\mathrm{d}{x}}
∫
⋯
∫
−
∞
+
∞
f
d
x
∰
Ω
P
d
x
d
y
d
z
+
Q
d
y
d
z
d
t
\displaystyle{\oiiint\limits_{Ω}P\mathrm{d}{x\mathrm{d}y\mathrm{d}z}+Q\mathrm{d}{y\mathrm{d}z\mathrm{d}t}}
Ω
∭
P
d
x
d
y
d
z
+
Q
d
y
d
z
d
t
∫
0
2
π
∫
0
π
∫
0
R
f
d
r
d
φ
d
θ
\displaystyle{\int\nolimits_{0}^{2π}\displaystyle{\int\nolimits_{0}^{π}\displaystyle{\int\nolimits_{0}^{R}f\,\mathrm{d}{r}}\,\mathrm{d}{φ}}\,\mathrm{d}{θ}}
∫
0
2
π
∫
0
π
∫
0
R
f
d
r
d
φ
d
θ
∫
0
1
d
x
∫
0
x
d
y
∫
0
z
(
x
,
y
)
f
(
x
,
y
,
z
)
d
z
\displaystyle{\int\nolimits_{0}^{1}\,\mathrm{d}{x}}\displaystyle{\int\nolimits_{0}^{x}\,\mathrm{d}{y}}\displaystyle{\int\nolimits_{0}^{z(x,y)}f(x,y,z)\,\mathrm{d}{z}}
∫
0
1
d
x
∫
0
x
d
y
∫
0
z
(
x
,
y
)
f
(
x
,
y
,
z
)
d
z
∫
0
2
π
d
θ
∫
0
θ
f
d
ρ
\displaystyle{\int\nolimits_{0}^{2π}\,\mathrm{d}{θ}}\displaystyle{\int\nolimits_{0}^{θ}f\,\mathrm{d}{ρ}}
∫
0
2
π
d
θ
∫
0
θ
f
d
ρ
∫
0
2
π
d
θ
∫
0
π
d
φ
∫
0
R
f
(
r
,
φ
,
θ
)
d
r
\displaystyle{\int\nolimits_{0}^{2π}\,\mathrm{d}{θ}}\displaystyle{\int\nolimits_{0}^{π}\,\mathrm{d}{φ}}\displaystyle{\int\nolimits_{0}^{R}f(r,φ,θ)\,\mathrm{d}{r}}
∫
0
2
π
d
θ
∫
0
π
d
φ
∫
0
R
f
(
r
,
φ
,
θ
)
d
r
∫
0
2
π
d
θ
f
(
ρ
,
θ
)
∣
ρ
=
a
ρ
=
0
\displaystyle{\int\nolimits_{0}^{2π}\,\mathrm{d}{θ}}f(ρ,θ)\LARGE|\normalsize\substack{ρ=a\\\\ ρ=0}
∫
0
2
π
d
θ
f
(
ρ
,
θ
)
∣
ρ
=
a
ρ
=
0
1
2
3
4
\begin{smallmatrix}1 & 2 \\ 3 & 4 \end{smallmatrix}
1
3
2
4
1
2
3
4
\begin{matrix}1 & 2 \\ 3 & 4 \end{matrix}
1
3
2
4
0
1
0
0
1
1
1
0
\left. \begin{array}{c:cc} & 0 & 1 \\ \hdashline 0 & 0 & 1 \\ 1 & 1 & 0 \end{array} \right.
0
1
0
0
1
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1
0
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\left. \begin{array}{c:c}1 & 2 \\ \hdashline 3 & 4 \end{array} \right.
1
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\left. \begin{array}{cc:cc}1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \end{array} \right.
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1
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\begin{aligned} & 1\\ & 2\\ & 3 \end{aligned}
1
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\begin{aligned} 1 & 2\\ & 3 \end{aligned}
1
2
3
\\
\\ ~ \\ ~
∑
0
<
i
<
m
0
<
j
<
n
\sum_{\substack{0<i<m\\0<j<n}}
0
<
i
<
m
0
<
j
<
n
∑
p
A
p\phantom{A}
p
A
h
p
0
hp\hphantom{0}
h
p
0
v
p
A
vp\vphantom{A}
v
p
A
t
a
g
1
A
tag{1}{A}
t
a
g
1
A
t
a
g
∗
2
B
tag*{2}{B}
t
a
g
∗
2
B
π
+
4
\def\zzllrr#1#2{{#1}+{#2}}\zzllrr{\pi}{4}
π
+
4
♡
♡
\newcommand\test[2]{\color{#1}{\heartsuit}\color{#2}{\heartsuit}} \test{red}{blue}
♡
♡
[
1
2
3
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]
\small \begin{bmatrix}1 & 2 \\ 3 & 4 \end{bmatrix}
[
1
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2
4
]
[
1
2
3
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]
\small \left[ \begin{array}{cc}1 & 2 \\ 3 & 4 \end{array} \right]
[
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2
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]
[
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]
\small \left[ \begin{array}{cc}1 & 2 \\ 3 & 4 \end{array} \right]
[
1
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2
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]
[
1
2
3
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]
\small \left[ \begin{array}{c:c}1 & 2 \\ \hdashline 3 & 4 \end{array} \right]
[
1
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]
[
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\small \left[ \begin{array}{cc:cc}1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \end{array} \right]
[
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3
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8
]
[
1
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3
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]
→
[
2
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1
[
5
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]
\small \begin{aligned} & ~ \quad \begin{bmatrix}1 & 2 \\ 3 & 4 \end{bmatrix} \\ & \xrightarrow{}[2]{1}\begin{bmatrix}5 & 6 \\ 7 & 8 \end{bmatrix} \end{aligned}
[
1
3
2
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]
[
2
]
1
[
5
7
6
8
]
[
1
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7
8
]
→
[
2
]
1
[
1
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3
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8
]
\small \begin{aligned} & ~ \quad \left[ \begin{array}{cc:cc}1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \end{array} \right] \\ & \xrightarrow{}[2]{1}\left[ \begin{array}{cc:cc}1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \end{array} \right] \end{aligned}
[
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[
a
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31
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a
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]
\small \begin{bmatrix}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix}
[
a
11
a
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a
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a
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a
13
a
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a
33
]
[
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a
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⋯
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a
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a
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⋯
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⋮
⋮
⋮
⋱
⋮
a
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1
a
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2
a
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3
⋯
a
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n
]
\small \begin{bmatrix}a_{11} & a_{12} & a_{13} & ⋯ & a_{1n} \\ a_{21} & a_{22} & a_{23} & ⋯ & a_{2n} \\ a_{31} & a_{32} & a_{33} & ⋯ & a_{3n} \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ a_{n1} & a_{n2} & a_{n3} & ⋯ & a_{nn} \end{bmatrix}
a
11
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31
⋮
a
n
1
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32
⋮
a
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⋮
a
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3
⋯
⋯
⋯
⋱
⋯
a
1
n
a
2
n
a
3
n
⋮
a
nn
∣
1
2
3
4
∣
\small \begin{vmatrix}1 & 2 \\ 3 & 4\end{vmatrix}
1
3
2
4
∣
1
2
3
4
∣
\small \begin{vmatrix}1 & 2 \\ 3 & 4\end{vmatrix}
1
3
2
4
∥
1
2
3
4
∥
\small \begin{Vmatrix}1 & 2 \\ 3 & 4 \end{Vmatrix}
1
3
2
4
∣
1
2
2
4
∣
=
[
2
n
d
]
1
s
t
0
\small \begin{aligned} & ~ \quad \begin{vmatrix}1 & 2 \\ 2 & 4\end{vmatrix} \\ & \xlongequal{}[2nd]{1st}0 \end{aligned}
1
2
2
4
[
2
n
d
]
1
s
t
0
∣
1
2
3
4
∣
=
[
2
n
d
]
1
s
t
∣
5
6
7
8
∣
\small \begin{aligned} & ~ \quad \begin{vmatrix}1 & 2 \\ 3 & 4\end{vmatrix} \\ & \xlongequal{}[2nd]{1st}\begin{vmatrix}5 & 6 \\ 7 & 8\end{vmatrix} \end{aligned}
1
3
2
4
[
2
n
d
]
1
s
t
5
7
6
8
∣
a
b
c
a
b
⋱
⋱
⋱
c
a
b
c
a
∣
\small \begin{vmatrix}a & b & & & \\ c & a & b & & \\ & ⋱ & ⋱ & ⋱ & \\ & & c & a & b \\ & & & c & a\end{vmatrix}
a
c
b
a
⋱
b
⋱
c
⋱
a
c
b
a
\small \begin{vmatrix}a & & & & & b \\ & ⋱ & & & \kern3mu \raisebox2mu{.}\kern1mu\raisebox7mu{.}\kern1mu\raisebox13mu{.}\kern4mu & \\ & & a & b & & \\ & & c & d & & \\ & \kern3mu \raisebox2mu{.}\kern1mu\raisebox7mu{.}\kern1mu\raisebox13mu{.}\kern4mu & & & ⋱ & \\ c & & & & & d\end{vmatrix}
∣
a
11
a
12
a
13
⋯
a
1
n
a
21
a
22
a
23
⋯
a
2
n
a
31
a
32
a
33
⋯
a
3
n
⋮
⋮
⋮
⋱
⋮
a
n
1
a
n
2
a
n
3
⋯
a
n
n
∣
\small \begin{vmatrix}a_{11} & a_{12} & a_{13} & ⋯ & a_{1n} \\ a_{21} & a_{22} & a_{23} & ⋯ & a_{2n} \\ a_{31} & a_{32} & a_{33} & ⋯ & a_{3n} \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ a_{n1} & a_{n2} & a_{n3} & ⋯ & a_{nn}\end{vmatrix}
a
11
a
21
a
31
⋮
a
n
1
a
12
a
22
a
32
⋮
a
n
2
a
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a
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⋮
a
n
3
⋯
⋯
⋯
⋱
⋯
a
1
n
a
2
n
a
3
n
⋮
a
nn
∣
1
1
1
⋯
1
a
1
a
2
a
3
⋯
a
n
a
1
2
a
2
2
a
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2
⋯
a
n
2
⋮
⋮
⋮
⋱
⋮
a
1
n
−
1
a
2
n
−
1
a
3
n
−
1
⋯
a
n
n
−
1
∣
\small \def\arraystretch{2}\begin{vmatrix}1 & 1 & 1 & ⋯ & 1 \\ a_1 & a_2 & a_3 & ⋯ & a_n \\ a_1^2 & a_2^2 & a_3^2 & ⋯ & a_n^2 \\ ⋮ & ⋮ & ⋮ & ⋱ & ⋮ \\ a_1^{n-1} & a_2^{n-1} & a_3^{n-1} & ⋯ & a_n^{n-1}\end{vmatrix}
1
a
1
a
1
2
⋮
a
1
n
−
1
1
a
2
a
2
2
⋮
a
2
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1
1
a
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3
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a
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a
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2
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a
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−
1
{
1
2
\small \begin{cases} 1 \\ 2 \end{cases}
{
1
2
{
1
2
3
4
\small \begin{cases} 1 & 2 \\ 3 & 4 \end{cases}
{
1
3
2
4
{
1
2
3
4
}
\small \begin{Bmatrix}1 & 2 \\ 3 & 4 \end{Bmatrix}
{
1
3
2
4
}
1
2
}
\small \left. \begin{array}{c}1 \\ 2 \end{array} \right\}
1
2
}
{
1
2
3
4
}
\small \left\{ \begin{array}{cc}1 & 2 \\ 3 & 4 \end{array} \right\}
{
1
3
2
4
}
{
1
x
+
2
y
=
3
4
x
−
5
y
=
6
\small \left\{\begin{alignedat}{6}1 & x & +2 & y & & = & 3\\ 4 & x & -5 & y & & = & 6\end{alignedat}\right.
{
1
4
x
x
+
2
−
5
y
y
=
=
3
6
{
1
x
+
2
y
≥
3
4
x
−
5
y
≤
6
\small \left\{\begin{alignedat}{6}1 & x & +2 & y & & ≥ & 3\\ 4 & x & -5 & y & & ≤ & 6\end{alignedat}\right.
{
1
4
x
x
+
2
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5
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y
≥
≤
3
6
(
x
2
)
\left( x^2\right)
(
x
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x
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\left\langle x^2\right\rangle
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[
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[
x
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x
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{
x
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x
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\left/ x^2\right\backslash
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x
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\left| x^2\right|
x
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x
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‖
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x
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\left\Updownarrow x^2\right\Updownarrow
⇓
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(
x
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\left( x,y\right.
(
x
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\left. x,y\right)
x
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(
x
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(
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[
x
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[
x
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(
x
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(
x
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<
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⟨
x
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<
a
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<
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(
a
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(
a
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(
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\big(\big)
(
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(
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\Big(\Big)
(
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(
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\bigg(\bigg)
(
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\Bigg(\Bigg)
(
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[
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\big[\big]
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[
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{
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{
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(
2
n
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{2n \choose n}
(
n
2
n
)
(
2
n
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\binom{2n}{n}
(
n
2
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(
2
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\tbinom{2n}{n}
(
n
2
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(
2
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\dbinom{2n}{n}
(
n
2
n
)
(
1
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\genfrac(){}{1}{1}{2}
(
2
1
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(
1
2
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\genfrac(){0pt}{1}{1}{2}
(
2
1
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(
1
2
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\genfrac(){1pt}{1}{1}{2}
(
2
1
)
[
1
2
]
1 \brack 2
[
2
1
]
{
1
2
}
1 \brace 2
{
2
1
}
(
1
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)
\genfrac(){0pt}{0}{1}{2}
(
2
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(
1
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\genfrac(){}{0}{1}{2}
(
2
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1
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(
2
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(
1
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)
3
\left( \frac{\displaystyle{}1}{\displaystyle{}2}\right) ^{3}
(
2
1
)
3
a
‾
\overline{a}
a
a
→
\overrightarrow{a}
a
a
↔
\overleftrightarrow{a}
a
a
←
\overleftarrow{a}
a
a
‾
\underline{a}
a
a
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\underrightarrow{a}
a
a
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\underleftrightarrow{a}
a
a
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\underleftarrow{a}
a
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\overleftharpoon{a}
a
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\overrightharpoon{a}
a
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\widehat{a}
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\widecheck{a}
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\overlinesegment{a}
a
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\overbrace{a}
a
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\overgroup{a}
a
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\widetilde{a}
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A
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A
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\cancel{1}
1
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1
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1
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\not{1}
1
1
\boxed{\textbf{1}}
1
F
\boxed{\mathfrak{F}}
F
A
\fbox{A}
A
α
α
α
β
β
β
γ
γ
γ
δ
δ
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ε
ε
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ϝ
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Ψ
Z
Ζ
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ℵ
ℵ
ℵ
ℶ
ℶ
ℶ
ℷ
ℷ
ℷ
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ℸ
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KaTeX
\KaTeX
K
A
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LaTeX
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L
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T
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boldsymbol
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ma
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→
[
2
]
1
\xrightarrow{}[2]{1}
[
2
]
1
↔
[
2
]
1
\xleftrightarrow{}[2]{1}
[
2
]
1
←
[
2
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1
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[
2
]
1
↦
[
2
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1
\xmapsto{}[2]{1}
[
2
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1
⟶
1
\stackrel{1}{\longrightarrow}
⟶
1
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[
2
]
1
\xhookleftarrow{}[2]{1}
[
2
]
1
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[
2
]
1
\xhookrightarrow{}[2]{1}
[
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LaTeX History中文
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⪋
:
\lesseqqgtr
≶
:
\lessgtr
≲
:
\lesssim
⊨
:
\vDash
⊸
:
\multimap
∋
:
\owns
‖
:
\parallel
⋔
:
\pitchfork
≺
:
\prec
⪷
:
\precapprox
≼
:
\preccurlyeq
⪯
:
\preceq
≾
:
\precsim
≓
:
\risingdotseq
∥
:
\lVert
∼
:
\thicksim
⌣
:
\smile
⋐
:
\Subset
⫅
:
\subseteqq
≻
:
\succ
⪸
:
\succapprox
≽
:
\succcurlyeq
⪰
:
\succeq
≿
:
\succsim
⋑
:
\Supset
⫆
:
\supseteqq
⊴
:
\trianglelefteq
≜
:
\triangleq
⊵
:
\trianglerighteq
△
:
\vartriangle
▽
:
\triangledown
◃
:
\triangleleft
▹
:
\triangleright
⊲
:
\lhd
⊳
:
\rhd
▲
:
\blacktriangle
▼
:
\blacktriangledown
◀
:
\blacktriangleleft
▶
:
\blacktriangleright
⋋
:
\leftthreetimes
⋌
:
\rightthreetimes
⊢
:
\vdash
⊩
:
\Vdash
⊪
:
\Vvdash
⪊
:
\gnapprox
⪈
:
\gneq
≩
:
\gneqq
⋧
:
\gnsim
:
\gvertneqq
⪉
:
\lnapprox
⪇
:
\lneq
≨
:
\lneqq
⋦
:
\lnsim
:
\lvertneqq
≆
:
\ncong
̸=
:
\neq
≱
:
\ngeq
:
\ngeqq
:
\ngeqslant
≰
:
\nleq
:
\nleqq
:
\nleqslant
≮
:
\nless
∈/
:
\notin
̸
:
\notni
∦
:
\nparallel
⊀
:
\nprec
⋠
:
\npreceq
:
\nshortmid
:
\nshortparallel
≁
:
\nsim
⊈
:
\nsubseteq
:
\nsubseteqq
⊁
:
\nsucc
⋡
:
\nsucceq
⊉
:
\nsupseteq
:
\nsupseteqq
⋪
:
\ntriangleleft
⋬
:
\ntrianglelefteq
⋫
:
\ntriangleright
⋭
:
\ntrianglerighteq
⊬
:
\nvdash
⊭
:
\nvDash
⊯
:
\nVDash
⊮
:
\nVdash
⪹
:
\precnapprox
⪵
:
\precneqq
⋨
:
\precnsim
⊊
:
\subsetneq
⫋
:
\subsetneqq
⪺
:
\succnapprox
⪶
:
\succneqq
⋩
:
\succnsim
⊋
:
\supsetneq
⫌
:
\supsetneqq
:
\varsubsetneq
:
\varsubsetneqq
:
\varsupsetneq
:
\varsupsetneqq
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