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https://github.com/nschloe/github-mathml-test
https://github.com/nschloe/github-mathml-test
Last synced: 22 days ago
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- Host: GitHub
- URL: https://github.com/nschloe/github-mathml-test
- Owner: nschloe
- Created: 2023-01-12T21:47:42.000Z (almost 2 years ago)
- Default Branch: main
- Last Pushed: 2023-01-12T21:48:34.000Z (almost 2 years ago)
- Last Synced: 2024-10-10T09:15:08.398Z (about 1 month ago)
- Size: 36.1 KB
- Stars: 2
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# 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