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https://github.com/nschloe/github-mathml-test


https://github.com/nschloe/github-mathml-test

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# GitHub MathML test

- Axiom of power set



A

P

B


[

B

P
⟺

C


(

C

B
⇒
C

A

)


]


- De Morgan's law:




Logic: 

¬

(

p

q

)

⟺

(

¬
p

)



(

¬
q

)






Boolean algebra: 




⋃

i
=
1

n


A
i


‾

=

⋂

i
=
1

n



A
i

‾


- Quadratic formula:



x
=



b
±


b
2


4
⁢
a
⁢
c



2
⁢
a



- Binomial coefficient:



C

(
n
,
k
)

=

C
k
n

=

C
k


n


=

(

n
k

)

=


n
!


k
!
⁢

(

n

k

)

!



- Sophomore's law




∫
0
1


x
x

⁢
ⅆ
x
=

∑

n
=
1





(


1

)


n
+
1


⁢

n


n



- Divergence




·

v
→

=


∂

v
x



∂
x


+


∂

v
y



∂
y


+


∂

v
z



∂
z



- Complex number



c
=







a


⏟

real

+




b
⁢
ⅈ


⏟

imaginary


⏞

complex number


- Moore determinant



M
=

[




α
1




α
1
q







α
1


q

n

1









α
2




α
2
q







α
2


q

n

1








⋮


⋮


⋱


⋮





α
m




α
m
q







α
m


q

n

1







]


- Sphere volume



    Spherical coordinates derivation of the volume of a sphere


(


4
3

⁢
π

R
3


)


.


The formula

S

for a sphere of radius

R

in spherical coordinates is:




S
=

{

0
≤
ϕ
≤
2
⁢
π



0
≤
θ
≤
π



0
≤
ρ
≤
R

}







Volume




=

∭
S


ρ
2

⁢
sin
⁡
θ
⁢
ⅆ
ρ
⁢
ⅆ
θ
⁢
ⅆ
ϕ







=

∫


0


2
⁢
π


ⅆ
ϕ
⁢

∫


0

π

sin
⁡
θ
⁢
ⅆ
θ
⁢

∫


0

R


ρ
2

⁢
ⅆ
ρ







=

ϕ


|


0



2
⁢
π


⁢

(


cos
⁡
θ

)



|


0



π



⁢

1
3

⁢

ρ
3



|


0



R









=

2
⁢
π
×
2
×

1
3

⁢

R
3








=


4
3

⁢
π

R
3






- Schwinger-Dyson equation






ψ


|


𝒯

{


δ

δ
ϕ


F
⁡

[
ϕ
]


}


|


ψ



=

ⅈ
⁢



ψ


|


𝒯

{

F
⁡

[
ϕ
]

⁢

δ

δ
ϕ


S
⁡

[
ϕ
]

}

|




ψ




- Differentiable manifold (tangent vector)




γ
1



γ
2

⟺

{




γ
1

⁡

(
0
)

=

γ
2

⁡

(
0
)

=
p
, and








ⅆ

ⅆ
t


⁡
ϕ
∘

γ
1

⁡

(
t
)



|



t
=
0


=




ⅆ

ⅆ
t


⁡
ϕ
∘

γ
2

⁡

(
t
)



|



t
=
0







- Cichoń's diagram







cov

(
ℒ
)



⟶


non

(
𝒦
)



⟶


cof

(
𝒦
)



⟶


cof

(
ℒ
)



⟶



2

ℵ
0







↑



↑



↑



↑






𝔟


⟶


𝔡






↑



↑






ℵ
1



⟶


add

(
ℒ
)



⟶


add

(
𝒦
)



⟶


cov

(
𝒦
)



⟶


non

(
ℒ
)






- Multiscripts & Greek alphabet





∏

𝔈
υ
τ

ρ
σ


𝔇
π
ο

ν
ξ



𝔄
δ
γ

α
β


𝔅
θ
η

ε
ζ



𝔉
ω
ψ

ϕ
χ


ℭ
μ
λ

ι
κ



- Nested roots





1
+


2
+


3
+


4
+


5
+


6
+


7
+

A
19


17


13


11


7


5


3



ⅇ
π


=

x
‴


- Nested matrices




(




(




a
1




a
2




a
3




a
4






a
5




a
6




a
7




a
8




)




(




b
1






b
2







b
3






b
4




)










0




(




c
1




c
2






c
3




c
4




)








)


- font sizes



scriptlevel :


3




2




1



0



1