wpmath0000007_15
Zubov's_method.html
{
x
:
v
(
x
)
<
1
}
\{x:\,v(x)<1\}
v
(
x
)
v(x)
x
′
=
f
(
x
)
,
t
∈
\R
x^{\prime}=f(x),t\in\R
\R
n
\R^{n}
f
(
0
)
=
0
f(0)=0
A
A
v
,
h
v,h
v
(
0
)
=
h
(
0
)
=
0
v(0)=h(0)=0
0
<
v
(
x
)
<
1
0<v(x)<1
x
∈
A
∖
{
0
}
x\in A\setminus\{0\}
h
>
0
h>0
\R
n
∖
{
0
}
\R^{n}\setminus\{0\}
γ
2
>
0
\gamma_{2}>0
γ
1
>
0
,
α
1
>
0
\gamma_{1}>0,\alpha_{1}>0
v
(
x
)
>
γ
1
,
h
(
x
)
>
α
1
v(x)>\gamma_{1},h(x)>\alpha_{1}
||
x
||
>
γ
2
||x||>\gamma_{2}
v
(
x
n
)
→
1
v(x_{n})\rightarrow 1
x
n
→
∂
A
x_{n}\rightarrow\partial A
||
x
n
||
→
∞
||x_{n}||\rightarrow\infty
∇
v
(
x
)
⋅
f
(
x
)
=
-
h
(
x
)
(
1
-
v
(
x
)
)
1
+
||
f
(
x
)
||
2
\nabla v(x)\cdot f(x)=-h(x)(1-v(x))\sqrt{1+||f(x)||^{2}}
v
(
0
)
=
0
v(0)=0
Ø_(disambiguation).html
∅
\varnothing
Σ-finite_measure.html
m
m
(
m
n
)
n
:
m
=
∑
n
∈
ℕ
m
n
(m_{n})_{n}:m=\sum_{n\in\mathbb{N}}m_{n}
ℕ
\mathbb{N}
H
=
⋃
n
∈
ℕ
V
n
H=\bigcup_{n\in\mathbb{N}}V^{n}
∞
\infty
\R
\scriptstyle\R
A
⊂
\R
\scriptstyle A\subset\R
μ
(
A
)
=
∞
\scriptstyle\mu(A)=\infty
A
⊂
\R
\scriptstyle A\subset\R
μ
(
A
)
=
∞
\scriptstyle\mu(A)=\infty
∑
n
=
1
∞
w
n
=
1.
\sum_{n=1}^{\infty}w_{n}=1.
ν
(
A
)
=
∑
n
=
1
∞
w
n
μ
(
A
∩
V
n
)
μ
(
V
n
)
\nu(A)=\sum_{n=1}^{\infty}w_{n}\frac{\mu(A\cap V_{n})}{\mu(V_{n})}
Ω-consistent_theory.html
∃
x
c
=
x
\exists x\,c=x
∀
w
[
B
(
0
,
w
)
∧
∀
x
(
B
(
x
,
w
)
→
B
(
x
+
1
,
w
)
)
→
∀
x
B
(
x
,
w
)
]
.
\forall w\,[B(0,w)\land\forall x\,(B(x,w)\to B(x+1,w))\to\forall x\,B(x,w)].
∀
w
[
B
(
0
,
w
)
∧
∀
x
(
B
(
x
,
w
)
→
B
(
x
+
1
,
w
)
)
→
B
(
n
,
w
)
]
\forall w\,[B(0,w)\land\forall x\,(B(x,w)\to B(x+1,w))\to B(n,w)]
∃
x
¬
P
(
x
)
\exists x\,\neg P(x)
P
(
0
)
,
P
(
1
)
,
P
(
2
)
,
…
P(0),P(1),P(2),\ldots
∀
x
(
N
(
x
)
→
P
(
x
)
)
\forall x\,(N(x)\to P(x))
∀
x
P
(
x
)
\forall x\,P(x)
T
+
RFN
T
+
Th
Π
2
0
(
ℕ
)
T+\mathrm{RFN}_{T}+\mathrm{Th}_{\Pi^{0}_{2}}(\mathbb{N})
Th
Π
2
0
(
ℕ
)
\mathrm{Th}_{\Pi^{0}_{2}}(\mathbb{N})
RFN
T
\mathrm{RFN}_{T}
∀
x
(
Prov
T
(
⌜
φ
(
x
˙
)
⌝
)
→
φ
(
x
)
)
\forall x\,(\mathrm{Prov}_{T}(\ulcorner\varphi(\dot{x})\urcorner)\to\varphi(x))
φ
\varphi
Σ
2
0
\Sigma^{0}_{2}
∂.html
∂
\partial
∂
z
∂
x
\frac{\partial z}{\partial x}
∂
(
x
,
y
,
z
)
∂
(
u
,
v
,
w
)
\frac{\partial(x,y,z)}{\partial(u,v,w)}