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$\forall A \exists P \forall B [B \in P ⟺ \forall C (C \in B \Rightarrow C \in A)]$	$\forall A \exists P \forall B [B \in P ⟺ \forall C (C \in B \Rightarrow C \in A)]$	$\forall A \exists P \forall B [B \in P ⟺ \forall C (C \in B \Rightarrow C \in A)]$
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
$C (n, k) = C_{k}^{n} = {}_{n}C_{k} = (\binom{n}{k}) = \frac{n!}{k! (n− k)!}$	$C (n, k) = C_{k}^{n} = {}_{n}C_{k} = (\binom{n}{k}) = \frac{n!}{k! (n− k)!}$	$C (n, k) = C_{k}^{n} = {}_{n}C_{k} = (\binom{n}{k}) = \frac{n!}{k! (n− k)!}$
$\int_{0}^{1} x^{x} ⅆ x = \sum_{n = 1}^{∞} {(- 1)}^{n + 1} n^{- n}$	$\int_{0}^{1} x^{x} ⅆ x = \sum_{n = 1}^{∞} {(- 1)}^{n + 1} n^{- n}$	$\int_{0}^{1} x^{x} ⅆ x = \sum_{n = 1}^{∞} {(- 1)}^{n + 1} n^{- n}$
$\nabla \cdot \vec{v} = \frac{\partial v_{x}}{\partial x} + \frac{\partial v_{y}}{\partial y} + \frac{\partial v_{z}}{\partial z}$	$\nabla \cdot \vec{v} = \frac{\partial v_{x}}{\partial x} + \frac{\partial v_{y}}{\partial y} + \frac{\partial v_{z}}{\partial z}$	$\nabla \cdot \vec{v} = \frac{\partial v_{x}}{\partial x} + \frac{\partial v_{y}}{\partial y} + \frac{\partial v_{z}}{\partial z}$
$c = \overset{complex number}{\overset{︷}{\underset{real}{\underset{︸}{a}} + \underset{imaginary}{\underset{︸}{b ⅈ}}}}$	$c = \overset{complex number}{\overset{︷}{\underset{real}{\underset{︸}{a}} + \underset{imaginary}{\underset{︸}{b ⅈ}}}}$	$c = \overset{complex number}{\overset{︷}{\underset{real}{\underset{︸}{a}} + \underset{imaginary}{\underset{︸}{b ⅈ}}}}$
$M = [\begin{matrix} α_{1} & α_{1}^{q} & \dots & α_{1}^{q^{n - 1}} \\ α_{2} & α_{2}^{q} & \dots & α_{2}^{q^{n - 1}} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ α_{m} & α_{m}^{q} & \dots & α_{m}^{q^{n - 1}} \end{matrix}]$	$M = [\begin{matrix} α_{1} & α_{1}^{q} & \dots & α_{1}^{q^{n - 1}} \\ α_{2} & α_{2}^{q} & \dots & α_{2}^{q^{n - 1}} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ α_{m} & α_{m}^{q} & \dots & α_{m}^{q^{n - 1}} \end{matrix}]$	$M = [\begin{matrix} α_{1} & α_{1}^{q} & \dots & α_{1}^{q^{n - 1}} \\ α_{2} & α_{2}^{q} & \dots & α_{2}^{q^{n - 1}} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ α_{m} & α_{m}^{q} & \dots & α_{m}^{q^{n - 1}} \end{matrix}]$
$\begin{aligned} Volume & = \underset{S}{∭} ρ^{2} sin θ ⅆ ρ ⅆ θ ⅆ ϕ \\ = \int_{0}^{2 π} ⅆ ϕ \int_{0}^{π} sin θ ⅆ θ \int_{0}^{R} ρ^{2} ⅆ ρ \\ = ϕ \|_{0}^{2 π} (- \cos θ) \|_{0}^{π} \frac{ρ^{3}}{3} \|_{0}^{R} \\ = (2 π) (2) (\frac{R^{3}}{3}) \\ = \frac{4}{3} π R^{3} \end{aligned}$	$\begin{aligned} Volume & = \underset{S}{∭} ρ^{2} sin θ ⅆ ρ ⅆ θ ⅆ ϕ \\ = \int_{0}^{2 π} ⅆ ϕ \int_{0}^{π} sin θ ⅆ θ \int_{0}^{R} ρ^{2} ⅆ ρ \\ = ϕ \|_{0}^{2 π} (- \cos θ) \|_{0}^{π} \frac{ρ^{3}}{3} \|_{0}^{R} \\ = (2 π) (2) (\frac{R^{3}}{3}) \\ = \frac{4}{3} π R^{3} \end{aligned}$	$\begin{aligned} Volume & = \underset{S}{∭} ρ^{2} sin θ ⅆ ρ ⅆ θ ⅆ ϕ \\ = \int_{0}^{2 π} ⅆ ϕ \int_{0}^{π} sin θ ⅆ θ \int_{0}^{R} ρ^{2} ⅆ ρ \\ = ϕ \|_{0}^{2 π} (- \cos θ) \|_{0}^{π} \frac{ρ^{3}}{3} \|_{0}^{R} \\ = (2 π) (2) (\frac{R^{3}}{3}) \\ = \frac{4}{3} π R^{3} \end{aligned}$
$〈ψ \|𝒯 \{\frac{δ}{δ ϕ} F [ϕ]\}\| ψ〉 = - ⅈ 〈ψ \|𝒯 \{F [ϕ] \frac{δ}{δ ϕ} S [ϕ]\}\| ψ〉$	$〈ψ \|𝒯 \{\frac{δ}{δ ϕ} F [ϕ]\}\| ψ〉 = - ⅈ 〈ψ \|𝒯 \{F [ϕ] \frac{δ}{δ ϕ} S [ϕ]\}\| ψ〉$	$〈ψ \|𝒯 \{\frac{δ}{δ ϕ} F [ϕ]\}\| ψ〉 = - ⅈ 〈ψ \|𝒯 \{F [ϕ] \frac{δ}{δ ϕ} S [ϕ]\}\| ψ〉$
$γ_{1} \equiv γ_{2} ⟺ \{\begin{cases} γ_{1} (0) = γ_{2} (0) = p, and \\ {\frac{ⅆ}{ⅆ t} ϕ \circ γ_{1} (t)\|}_{t = 0} = {\frac{ⅆ}{ⅆ t} ϕ \circ γ_{2} (t)\|}_{t = 0} \end{cases}$	$γ_{1} \equiv γ_{2} ⟺ \{\begin{cases} γ_{1} (0) = γ_{2} (0) = p, and \\ {\frac{ⅆ}{ⅆ t} ϕ \circ γ_{1} (t)\|}_{t = 0} = {\frac{ⅆ}{ⅆ t} ϕ \circ γ_{2} (t)\|}_{t = 0} \end{cases}$	$γ_{1} \equiv γ_{2} ⟺ \{\begin{cases} γ_{1} (0) = γ_{2} (0) = p, and \\ {\frac{ⅆ}{ⅆ t} ϕ \circ γ_{1} (t)\|}_{t = 0} = {\frac{ⅆ}{ⅆ t} ϕ \circ γ_{2} (t)\|}_{t = 0} \end{cases}$
$\begin{matrix} cov (ℒ) & ⟶ & non (𝒦) & ⟶ & cof (𝒦) & ⟶ & cof (ℒ) & ⟶ & 2^{ℵ_{0}} \\ ↑ & ↑ & ↑ & ↑ \\ 𝔟 & ⟶ & 𝔡 \\ ↑ & ↑ \\ ℵ_{1} & ⟶ & add (ℒ) & ⟶ & add (𝒦) & ⟶ & cov (𝒦) & ⟶ & non (ℒ) \end{matrix}$	$\begin{matrix} cov (ℒ) & ⟶ & non (𝒦) & ⟶ & cof (𝒦) & ⟶ & cof (ℒ) & ⟶ & 2^{ℵ_{0}} \\ ↑ & ↑ & ↑ & ↑ \\ 𝔟 & ⟶ & 𝔡 \\ ↑ & ↑ \\ ℵ_{1} & ⟶ & add (ℒ) & ⟶ & add (𝒦) & ⟶ & cov (𝒦) & ⟶ & non (ℒ) \end{matrix}$	$\begin{matrix} cov (ℒ) & ⟶ & non (𝒦) & ⟶ & cof (𝒦) & ⟶ & cof (ℒ) & ⟶ & 2^{ℵ_{0}} \\ ↑ & ↑ & ↑ & ↑ \\ 𝔟 & ⟶ & 𝔡 \\ ↑ & ↑ \\ ℵ_{1} & ⟶ & add (ℒ) & ⟶ & add (𝒦) & ⟶ & cov (𝒦) & ⟶ & non (ℒ) \end{matrix}$
${}_{{}_{α}^{β}𝔄_{δ}^{γ}}^{{}_{ε}^{ζ}𝔅_{θ}^{η}}\prod_{{}_{ρ}^{σ}𝔈_{υ}^{τ}}^{{}_{ν}^{ξ}𝔇_{π}^{ο}}_{{}_{ϕ}^{χ}𝔉_{ω}^{ψ}}^{{}_{ι}^{κ}𝔈_{μ}^{λ}}$	${}_{{}_{α}^{β}𝔄_{δ}^{γ}}^{{}_{ε}^{ζ}𝔅_{θ}^{η}}\prod_{{}_{ρ}^{σ}𝔈_{υ}^{τ}}^{{}_{ν}^{ξ}𝔇_{π}^{ο}}_{{}_{ϕ}^{χ}𝔉_{ω}^{ψ}}^{{}_{ι}^{κ}𝔈_{μ}^{λ}}$	${}_{{}_{α}^{β}𝔄_{δ}^{γ}}^{{}_{ε}^{ζ}𝔅_{θ}^{η}}\prod_{{}_{ρ}^{σ}𝔈_{υ}^{τ}}^{{}_{ν}^{ξ}𝔇_{π}^{ο}}_{{}_{ϕ}^{χ}𝔉_{ω}^{ψ}}^{{}_{ι}^{κ}𝔈_{μ}^{λ}}$
$\frac{\sqrt{1 + \sqrt[3]{2 + \sqrt[5]{3 + \sqrt[7]{4 + \sqrt[11]{5 + \sqrt[13]{6 + \sqrt[17]{7 + \sqrt[19]{A}}}}}}}}}{ⅇ^{π}} = x^{‴}$	$\frac{\sqrt{1 + \sqrt[3]{2 + \sqrt[5]{3 + \sqrt[7]{4 + \sqrt[11]{5 + \sqrt[13]{6 + \sqrt[17]{7 + \sqrt[19]{A}}}}}}}}}{ⅇ^{π}} = x^{‴}$	$\frac{\sqrt{1 + \sqrt[3]{2 + \sqrt[5]{3 + \sqrt[7]{4 + \sqrt[11]{5 + \sqrt[13]{6 + \sqrt[17]{7 + \sqrt[19]{A}}}}}}}}}{ⅇ^{π}} = x^{‴}$
$(\begin{matrix} (\begin{matrix} a_{1} & a_{2} & a_{3} & a_{4} \\ a_{5} & a_{6} & a_{7} & a_{8} \end{matrix}) & (\begin{matrix} b_{1} \\ b_{2} \\ b_{3} \\ b_{4} \end{matrix}) \\ \begin{matrix} 0 & (\begin{matrix} c_{1} & c_{2} \\ c_{3} & c_{4} \end{matrix}) \end{matrix} \end{matrix})$	$(\begin{matrix} (\begin{matrix} a_{1} & a_{2} & a_{3} & a_{4} \\ a_{5} & a_{6} & a_{7} & a_{8} \end{matrix}) & (\begin{matrix} b_{1} \\ b_{2} \\ b_{3} \\ b_{4} \end{matrix}) \\ \begin{matrix} 0 & (\begin{matrix} c_{1} & c_{2} \\ c_{3} & c_{4} \end{matrix}) \end{matrix} \end{matrix})$	$(\begin{matrix} (\begin{matrix} a_{1} & a_{2} & a_{3} & a_{4} \\ a_{5} & a_{6} & a_{7} & a_{8} \end{matrix}) & (\begin{matrix} b_{1} \\ b_{2} \\ b_{3} \\ b_{4} \end{matrix}) \\ \begin{matrix} 0 & (\begin{matrix} c_{1} & c_{2} \\ c_{3} & c_{4} \end{matrix}) \end{matrix} \end{matrix})$