TreeBlood arrays Test
A_{m,n} =   \begin{pmatrix}   a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\   a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\   \vdots  & \vdots  & \ddots & \vdots  \\   a_{m,1} & a_{m,2} & \cdots & a_{m,n}   \end{pmatrix}
 A m , n = ( a 1 , 1 a 1 , 2 ⋯ a 1 , n a 2 , 1 a 2 , 2 ⋯ a 2 , n ⋮ ⋮ ⋱ ⋮ a m , 1 a m , 2 ⋯ a m , n ) A_{m,n} = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix} A m , n = ( a 1 , 1 a 1 , 2 ⋯ a 1 , n a 2 , 1 a 2 , 2 ⋯ a 2 , n ⋮ ⋮ ⋱ ⋮ a m , 1 a m , 2 ⋯ a m , n ) A_{m,n} = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix} 
\begin{pmatrix} \begin{matrix} \begin{bmatrix} a_1 & a_2 & a_3 & a_4 \\ a_5 & a_6 & a_7 & a_8 \end{bmatrix} \\ 0 & \begin{Vmatrix} c_1 & c_2 \\ c_3 & c_4 \end{Vmatrix} \end{matrix} & \begin{Bmatrix} b_1 \\ b_2 \\ b_3 \\ b_4 \end{Bmatrix} \end{pmatrix}
 ( [ a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 ] 0 ‖ c 1 c 2 c 3 c 4 ‖ { b 1 b 2 b 3 b 4 } ) \begin{pmatrix} \begin{matrix} \begin{bmatrix} a_1 & a_2 & a_3 & a_4 \\ a_5 & a_6 & a_7 & a_8 \end{bmatrix} \\ 0 & \begin{Vmatrix} c_1 & c_2 \\ c_3 & c_4 \end{Vmatrix} \end{matrix} & \begin{Bmatrix} b_1 \\ b_2 \\ b_3 \\ b_4 \end{Bmatrix} \end{pmatrix} ( [ a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 ] 0 ‖ c 1 c 2 c 3 c 4 ‖ { b 1 b 2 b 3 b 4 } ) \begin{pmatrix} \begin{matrix} \begin{bmatrix} a_1 & a_2 & a_3 & a_4 \\ a_5 & a_6 & a_7 & a_8 \end{bmatrix} \\ 0 & \begin{Vmatrix} c_1 & c_2 \\ c_3 & c_4 \end{Vmatrix} \end{matrix} & \begin{Bmatrix} b_1 \\ b_2 \\ b_3 \\ b_4 \end{Bmatrix} \end{pmatrix} 
f'(x) = \begin{cases}
\lim_{c \to x} \dfrac{f(c) - f(x)}{c-x} & \text{(A)} \\ 
\lim_{h \to 0} \frac{f(x+h) - f(x)}{h} & \text{(B)} \\ 
\lim_{t \to 1} \frac{f(tx) - f(x)}{tx - x} & \text{(C)}
\end{cases}
 f ′ ( x ) = { lim c → x f ( c ) − f ( x ) c − x (A) lim h → 0 f ( x + h ) − f ( x ) h (B) lim t → 1 f ( t x ) − f ( x ) t x − x (C) f'(x) = \begin{cases} \lim_{c \to x} \dfrac{f(c) - f(x)}{c-x} & \text{(A)} \\ \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} & \text{(B)} \\ \lim_{t \to 1} \frac{f(tx) - f(x)}{tx - x} & \text{(C)} \end{cases} f ′ ( x ) = { lim c → x f ( c ) − f ( x ) c − x (A) lim h → 0 f ( x + h ) − f ( x ) h (B) lim t → 1 f ( t x ) − f ( x ) t x − x (C) f'(x) = \begin{cases} \lim_{c \to x} \dfrac{f(c) - f(x)}{c-x} & \text{(A)} \\ \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} & \text{(B)} \\ \lim_{t \to 1} \frac{f(tx) - f(x)}{tx - x} & \text{(C)} \end{cases} 
\begin{align}
\mathrm{Volume} & =\iiint_S\! \rho^2 \sin\theta \,\mathrm{d}\rho \,\mathrm{d}\theta \,\mathrm{d}\phi \\
& =\int_0^{2 \pi }\! \mathrm{d}\phi \,\int_0^{ \pi }\! \sin\theta \,\mathrm{d}\theta \,\int_0^R\! \rho^2 \mathrm{d}\rho \\
& =\phi |_0^{2\pi}\ (-\cos\theta) |_0^{ \pi }\ \dfrac 1 3 \rho^3 |_0^R \\
& =2\pi \times 2 \times \frac 1 3 R^3 \\
& =\frac 4 3 \pi R^3
\end{align}
 V o l u m e = ∭ 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 \begin{align} \mathrm{Volume} & =\iiint_S\! \rho^2 \sin\theta \,\mathrm{d}\rho \,\mathrm{d}\theta \,\mathrm{d}\phi \\ & =\int_0^{2 \pi }\! \mathrm{d}\phi \,\int_0^{ \pi }\! \sin\theta \,\mathrm{d}\theta \,\int_0^R\! \rho^2 \mathrm{d}\rho \\ & =\phi |_0^{2\pi}\ (-\cos\theta) |_0^{ \pi }\ \dfrac 1 3 \rho^3 |_0^R \\ & =2\pi \times 2 \times \frac 1 3 R^3 \\ & =\frac 4 3 \pi R^3 \end{align} V o l u m e = ∭ 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 \begin{align} \mathrm{Volume} & =\iiint_S\! \rho^2 \sin\theta \,\mathrm{d}\rho \,\mathrm{d}\theta \,\mathrm{d}\phi \\ & =\int_0^{2 \pi }\! \mathrm{d}\phi \,\int_0^{ \pi }\! \sin\theta \,\mathrm{d}\theta \,\int_0^R\! \rho^2 \mathrm{d}\rho \\ & =\phi |_0^{2\pi}\ (-\cos\theta) |_0^{ \pi }\ \dfrac 1 3 \rho^3 |_0^R \\ & =2\pi \times 2 \times \frac 1 3 R^3 \\ & =\frac 4 3 \pi R^3 \end{align} 
\begin{array}{ccccccccccc}
                        &                 & \mathrm{cov}({\mathcal L})     & \longrightarrow &\mathrm{non}({\mathcal K}) & \longrightarrow & \mathrm{cof}({\mathcal K}) & \longrightarrow &\mathrm{cof}({\mathcal L})     & \longrightarrow & 2^{\aleph_0} \\
                        &                 & \multirow{3}{*}{\uparrow}      &                 &\uparrow                   &                 & \uparrow                   &                 &\multirow{3}{*}{\uparrow}       &                 & \\
                        &                 &                                &                 &{\mathfrak b}              & \longrightarrow & {\mathfrak d}              &                 &                               &                 & \\
                        &                 &                                &                 &\uparrow                   &                 & \uparrow                   &                 &                               &                 & \\
\aleph_1                & \longrightarrow & \mathrm{add}({\mathcal L})     & \longrightarrow &\mathrm{add}({\mathcal K}) & \longrightarrow & \mathrm{cov}({\mathcal K}) & \longrightarrow &\mathrm{non}({\mathcal L})     &                 &
\end{array}
 c o v ( ℒ︀ ) ⟶ n o n ( 𝒦︀ ) ⟶ c o f ( 𝒦︀ ) ⟶ c o f ( ℒ︀ ) ⟶ 2 ℵ 0 ↑ ↑ ↑ ↑ 𝔟 ⟶ 𝔡 ↑ ↑ ℵ 1 ⟶ a d d ( ℒ︀ ) ⟶ a d d ( 𝒦︀ ) ⟶ c o v ( 𝒦︀ ) ⟶ n o n ( ℒ︀ ) \begin{array}{ccccccccccc} & & \mathrm{cov}({\mathcal L}) & \longrightarrow &\mathrm{non}({\mathcal K}) & \longrightarrow & \mathrm{cof}({\mathcal K}) & \longrightarrow &\mathrm{cof}({\mathcal L}) & \longrightarrow & 2^{\aleph_0} \\ & & \multirow{3}{*}{\uparrow} & &\uparrow & & \uparrow & &\multirow{3}{*}{\uparrow} & & \\ & & & &{\mathfrak b} & \longrightarrow & {\mathfrak d} & & & & \\ & & & &\uparrow & & \uparrow & & & & \\ \aleph_1 & \longrightarrow & \mathrm{add}({\mathcal L}) & \longrightarrow &\mathrm{add}({\mathcal K}) & \longrightarrow & \mathrm{cov}({\mathcal K}) & \longrightarrow &\mathrm{non}({\mathcal L}) & & \end{array} c o v ( ℒ︀ ) ⟶ n o n ( 𝒦︀ ) ⟶ c o f ( 𝒦︀ ) ⟶ c o f ( ℒ︀ ) ⟶ 2 ℵ 0 ↑ ↑ ↑ ↑ 𝔟 ⟶ 𝔡 ↑ ↑ ℵ 1 ⟶ a d d ( ℒ︀ ) ⟶ a d d ( 𝒦︀ ) ⟶ c o v ( 𝒦︀ ) ⟶ n o n ( ℒ︀ ) \begin{array}{ccccccccccc} & & \mathrm{cov}({\mathcal L}) & \longrightarrow &\mathrm{non}({\mathcal K}) & \longrightarrow & \mathrm{cof}({\mathcal K}) & \longrightarrow &\mathrm{cof}({\mathcal L}) & \longrightarrow & 2^{\aleph_0} \\ & & \multirow{3}{*}{\uparrow} & &\uparrow & & \uparrow & &\multirow{3}{*}{\uparrow} & & \\ & & & &{\mathfrak b} & \longrightarrow & {\mathfrak d} & & & & \\ & & & &\uparrow & & \uparrow & & & & \\ \aleph_1 & \longrightarrow & \mathrm{add}({\mathcal L}) & \longrightarrow &\mathrm{add}({\mathcal K}) & \longrightarrow & \mathrm{cov}({\mathcal K}) & \longrightarrow &\mathrm{non}({\mathcal L}) & & \end{array} 
\begin{array}{}
\multicolumn{3}{}{\rightarrow} & & & \multirow{3}{}{\downarrow} \\ 
\multirow{3}{}{\uparrow}&\multirow{2}{}{\multicolumn{2}{l}{\huge\circlearrowright}}&& \\
&&& \\
& \multicolumn{3}{}{\leftarrow}&&
\end{array}
 → ↓ ↑ ↻ ← \begin{array}{} \multicolumn{3}{}{\rightarrow} & & & \multirow{3}{}{\downarrow} \\ \multirow{3}{}{\uparrow}&\multirow{2}{}{\multicolumn{2}{l}{\huge\circlearrowright}}&& \\ &&& \\ & \multicolumn{3}{}{\leftarrow}&& \end{array} → ↓ ↑ ↻ ← \begin{array}{} \multicolumn{3}{}{\rightarrow} & & & \multirow{3}{}{\downarrow} \\ \multirow{3}{}{\uparrow}&\multirow{2}{}{\multicolumn{2}{l}{\huge\circlearrowright}}&& \\ &&& \\ & \multicolumn{3}{}{\leftarrow}&& \end{array} 
\begin{array}{c}
{\large \text{Generalized Product Rule:}} \\
\displaystyle \dv{x} \left[\prod_{i=1}^k f_i(x)\right] = \sum_{j=1}^k\left(f^\prime_j(x)\prod_\substack{i=1\\i\not=j}^kf_i(x)\right)
\end{array}
 Generalized Product Rule: dv x [ ∏ i = 1 k f i ( x ) ] = ∑ j = 1 k ( f j ′ ( x ) ∏ i = 1 i ≠ j k f i ( x ) ) \begin{array}{c} {\large \text{Generalized Product Rule:}} \\ \displaystyle \dv{x} \left[\prod_{i=1}^k f_i(x)\right] = \sum_{j=1}^k\left(f^\prime_j(x)\prod_\substack{i=1\\i\not=j}^kf_i(x)\right) \end{array} Generalized Product Rule: dv x [ ∏ i = 1 k f i ( x ) ] = ∑ j = 1 k ( f j ′ ( x ) ∏ i = 1 i ≠ j k f i ( x ) ) \begin{array}{c} {\large \text{Generalized Product Rule:}} \\ \displaystyle \dv{x} \left[\prod_{i=1}^k f_i(x)\right] = \sum_{j=1}^k\left(f^\prime_j(x)\prod_\substack{i=1\\i\not=j}^kf_i(x)\right) \end{array}
TreeBlood bad inputs Test
{(a}
 ( a {(a} ( a {(a} 
{x\not}
x not {x\not} x not {x\not}
TreeBlood basic Test
%this is a comment
0123456789
 0123456789 %this is a comment 0123456789 0123456789 %this is a comment 0123456789 
\forall A \, \exists P \, \forall B \, [B \in P \Leftrightarrow \forall C \, (C \in B \Rightarrow C \in A)]
 ∀ A ∃ P ∀ B [ B ∈ P ⇔ ∀ C ( C ∈ B ⇒ C ∈ A ) ] \forall A \, \exists P \, \forall B \, [B \in P \Leftrightarrow \forall C \, (C \in B \Rightarrow C \in A)] ∀ A ∃ P ∀ B [ B ∈ P ⇔ ∀ C ( C ∈ B ⇒ C ∈ A ) ] \forall A \, \exists P \, \forall B \, [B \in P \Leftrightarrow \forall C \, (C \in B \Rightarrow C \in A)] 
a' b'' c''' d'''' e''''' f'''''' g''''''' h'''''''' i''''''''' j''''''''''
 a ′ b ″ c ‴ d ⁗ e ⁗ ′ f ⁗ ″ g ⁗ ‴ h ⁗ ⁗ i ⁗ ⁗ ′ j ⁗ ⁗ ″ a' b'' c''' d'''' e''''' f'''''' g''''''' h'''''''' i''''''''' j'''''''''' a ′ b ″ c ‴ d ⁗ e ⁗ ′ f ⁗ ″ g ⁗ ‴ h ⁗ ⁗ i ⁗ ⁗ ′ j ⁗ ⁗ ″ a' b'' c''' d'''' e''''' f'''''' g''''''' h'''''''' i''''''''' j'''''''''' 
\forall n \in \mathbb{N} \exists \; x \; \in \mathbb{R} \; : \; n^x \not\in \mathbb{Q}
 ∀ n ∈ ℕ ∃ x ∈ ℝ : n x ∉ ℚ \forall n \in \mathbb{N} \exists \; x \; \in \mathbb{R} \; : \; n^x \not\in \mathbb{Q} ∀ n ∈ ℕ ∃ x ∈ ℝ : n x ∉ ℚ \forall n \in \mathbb{N} \exists \; x \; \in \mathbb{R} \; : \; n^x \not\in \mathbb{Q} 
c = \overbrace {     \underbrace{\;\;\;\;\; a \;\;\;\;}_\text{real}     +     \underbrace{\;\;\;\;\; b\mathrm{i} \;\;\;\;}_\text{imaginary} }^\text{complex number}
c = a ⏟ real + b i ⏟ imaginary ⏞ complex number c = \overbrace { \underbrace{\;\;\;\;\; a \;\;\;\;}_\text{real} + \underbrace{\;\;\;\;\; b\mathrm{i} \;\;\;\;}_\text{imaginary} }^\text{complex number} c = a ⏟ real + b i ⏟ imaginary ⏞ complex number c = \overbrace { \underbrace{\;\;\;\;\; a \;\;\;\;}_\text{real} + \underbrace{\;\;\;\;\; b\mathrm{i} \;\;\;\;}_\text{imaginary} }^\text{complex number} 
\mathrm{\nabla} \cdot \vec {v} = \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{\partial z}
 ∇ ⋅ v ⃗ = ∂ v x ∂ x + ∂ v y ∂ y + ∂ v z ∂ z \mathrm{\nabla} \cdot \vec {v} = \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{\partial z} ∇ ⋅ v ⃗ = ∂ v x ∂ x + ∂ v y ∂ y + ∂ v z ∂ z \mathrm{\nabla} \cdot \vec {v} = \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{\partial z} 
\left\langle\psi\left|\mathcal{T}\left\{\frac{\delta}{\delta\phi}F[\phi]\right\}\right|\psi\right\rangle = -\mathrm{i}\left\langle\psi\left|\mathcal{T}\left\{F[\phi]\frac{\delta}{\delta\phi}S[\phi]\right\}\right|\psi\right\rangle
 ⟨ ψ | 𝒯︀ { δ δ ϕ F [ ϕ ] } | ψ ⟩ = − i ⟨ ψ | 𝒯︀ { F [ ϕ ] δ δ ϕ S [ ϕ ] } | ψ ⟩ \left\langle\psi\left|\mathcal{T}\left\{\frac{\delta}{\delta\phi}F[\phi]\right\}\right|\psi\right\rangle = -\mathrm{i}\left\langle\psi\left|\mathcal{T}\left\{F[\phi]\frac{\delta}{\delta\phi}S[\phi]\right\}\right|\psi\right\rangle ⟨ ψ | 𝒯︀ { δ δ ϕ F [ ϕ ] } | ψ ⟩ = − i ⟨ ψ | 𝒯︀ { F [ ϕ ] δ δ ϕ S [ ϕ ] } | ψ ⟩ \left\langle\psi\left|\mathcal{T}\left\{\frac{\delta}{\delta\phi}F[\phi]\right\}\right|\psi\right\rangle = -\mathrm{i}\left\langle\psi\left|\mathcal{T}\left\{F[\phi]\frac{\delta}{\delta\phi}S[\phi]\right\}\right|\psi\right\rangle 
\mathscr{L} \text{ vs. } \mathcal{L}
 ℒ︁  vs.  ℒ︀ \mathscr{L} \text{ vs. } \mathcal{L} ℒ︁  vs.  ℒ︀ \mathscr{L} \text{ vs. } \mathcal{L} 
\binom{n}{k/2} = \frac{n!}{n!(n-k/2)!}
 ( n k / 2 ) = n ! n ! ( n − k / 2 ) ! \binom{n}{k/2} = \frac{n!}{n!(n-k/2)!} ( n k / 2 ) = n ! n ! ( n − k / 2 ) ! \binom{n}{k/2} = \frac{n!}{n!(n-k/2)!} 
a \not{=} b \quad \not{\alpha}=\not{b} \quad \not{abc}
 a ≠ b α̸ = b̸ a b c a \not{=} b \quad \not{\alpha}=\not{b} \quad \not{abc} a ≠ b α̸ = b̸ a b c a \not{=} b \quad \not{\alpha}=\not{b} \quad \not{abc} 
\frac{\sqrt{1 + \sqrt[3]{2 + \sqrt[5]{3 + \sqrt[7]{4 + \sqrt[11]{5 + \sqrt[13]{6 + \sqrt[17]{7 + \sqrt[19]{A}}}}}}}}}{\mathrm{e}^\pi} = x'''
 1 + 2 + 3 + 4 + 5 + 6 + 7 + A 19 17 13 11 7 5 3 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}}}}}}}}}{\mathrm{e}^\pi} = x''' 1 + 2 + 3 + 4 + 5 + 6 + 7 + A 19 17 13 11 7 5 3 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}}}}}}}}}{\mathrm{e}^\pi} = x''' 
\varphi=1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1+\cdots}}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}}}}}
φ = 1 + 1 1 + 1 1 + 1 1 + 1 1 + 1 1 + ⋯ = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + ⋯ \varphi=1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1+\cdots}}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}}}}} φ = 1 + 1 1 + 1 1 + 1 1 + 1 1 + 1 1 + ⋯ = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + ⋯ \varphi=1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1+\cdots}}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}}}}} 
\def\d{\mathrm{d}} \oint_C \vec{B}\circ \d\vec{l} = \mu_0 \left( I_{\text{enc}} + \varepsilon_0 \frac{\d}{\d t} \int_S {\vec{E} \circ \hat{n}}\; \d a \right)
 ∮ C B ⃗ ∘ d l ⃗ = μ 0 ( I enc + ε 0 d d t ∫ S E ⃗ ∘ n ^ d a ) \def\d{\mathrm{d}} \oint_C \vec{B}\circ \d\vec{l} = \mu_0 \left( I_{\text{enc}} + \varepsilon_0 \frac{\d}{\d t} \int_S {\vec{E} \circ \hat{n}}\; \d a \right) ∮ C B ⃗ ∘ d l ⃗ = μ 0 ( I enc + ε 0 d d t ∫ S E ⃗ ∘ n ^ d a ) \def\d{\mathrm{d}} \oint_C \vec{B}\circ \d\vec{l} = \mu_0 \left( I_{\text{enc}} + \varepsilon_0 \frac{\d}{\d t} \int_S {\vec{E} \circ \hat{n}}\; \d a \right)
TreeBlood chemistry Test
\ce{CO2 + C -> 2 CO}
 C O 2 + C → 2 C O \ce{CO2 + C -> 2 CO} C O 2 + C → 2 C O \ce{CO2 + C -> 2 CO} 
\ce{Hg^2+ ->[I-] HgI2 ->[I-] [Hg^{II}I4]^2-}
 Hg 2 + → I − Hg I 2 → I − [ Hg I I I 4 ] − 2 \ce{Hg^2+ ->[I-] HgI2 ->[I-] [Hg^{II}I4]^2-} Hg 2 + → I − Hg I 2 → I − [ Hg I I I 4 ] − 2 \ce{Hg^2+ ->[I-] HgI2 ->[I-] [Hg^{II}I4]^2-} 
\ce{H2O}
 H 2 O \ce{H2O} H 2 O \ce{H2O} 
\ce{Sb2O3}
 Sb 2 O 3 \ce{Sb2O3} Sb 2 O 3 \ce{Sb2O3} 
\ce{H+}
 H + \ce{H+} H + \ce{H+} 
\ce{CrO4^2-}
 Cr O 4 2 − \ce{CrO4^2-} Cr O 4 2 − \ce{CrO4^2-} 
\ce{[AgCl2]-}
 [ Ag Cl 2 ] − \ce{[AgCl2]-} [ Ag Cl 2 ] − \ce{[AgCl2]-} 
\ce{Y^99+}
 Y 99 + \ce{Y^99+} Y 99 + \ce{Y^99+} 
\ce{Y^{99+}}
 Y 99 + \ce{Y^{99+}} Y 99 + \ce{Y^{99+}} 
\ce{Fe^{II}Fe^{III}2O4}
 Fe I I Fe 2 I I I O 4 \ce{Fe^{II}Fe^{III}2O4} Fe I I Fe 2 I I I O 4 \ce{Fe^{II}Fe^{III}2O4} 
\ce{2H2O}
 2 H 2 O \ce{2H2O} 2 H 2 O \ce{2H2O} 
\ce{2 H2O}
 2 H 2 O \ce{2 H2O} 2 H 2 O \ce{2 H2O} 
\ce{0.5H2O}
 0.5 H 2 O \ce{0.5H2O} 0.5 H 2 O \ce{0.5H2O} 
\ce{1/2H2O}
 1 2 H 2 O \ce{1/2H2O} 1 2 H 2 O \ce{1/2H2O} 
\ce{(1/2)H2O}
 ( 1 / 2 ) H 2 O \ce{(1/2)H2O} ( 1 / 2 ) H 2 O \ce{(1/2)H2O} 
\ce{$n$H2O}
 n H 2 O \ce{$n$H2O} n H 2 O \ce{$n$H2O} 
\ce{^{227}_{90}Th+}
 90 227 Th + \ce{^{227}_{90}Th+} 90 227 Th + \ce{^{227}_{90}Th+} 
\ce{^227_90Th+}
 90 227 Th + \ce{^227_90Th+} 90 227 Th + \ce{^227_90Th+} 
\ce{^{0}_{-1}n^{-}}
 − 1 0 n − \ce{^{0}_{-1}n^{-}} − 1 0 n − \ce{^{0}_{-1}n^{-}} 
\ce{^0_-1n-}
 − 1 0 n − \ce{^0_-1n-} − 1 0 n − \ce{^0_-1n-} 
\ce{H{}^3HO}
 H 3 H O \ce{H{}^3HO} H 3 H O \ce{H{}^3HO} 
\ce{H^3HO}
 H 3 H O \ce{H^3HO} H 3 H O \ce{H^3HO} 
\ce{(NH4)2S}
 ( N H 4 ) 2 S \ce{(NH4)2S} ( N H 4 ) 2 S \ce{(NH4)2S} 
\ce{[\{(X2)3\}2]^3+}
 [ { ( X 2 ) 3 } 2 ] + 3 \ce{[\{(X2)3\}2]^3+} [ { ( X 2 ) 3 } 2 ] + 3 \ce{[\{(X2)3\}2]^3+} 
\ce{CH4 + 2 $\left( \ce{O2 + 79/21 N2} \right)$}
 C H 4 + 2 ( O 2 + 79 21 N 2 ) \ce{CH4 + 2 $\left( \ce{O2 + 79/21 N2} \right)$} C H 4 + 2 ( O 2 + 79 21 N 2 ) \ce{CH4 + 2 $\left( \ce{O2 + 79/21 N2} \right)$} 
\ce{H2(aq)}
 H 2 ( aq ) \ce{H2(aq)} H 2 ( aq ) \ce{H2(aq)} 
\ce{CO3^2-{}_{(aq)}}
 C O 3 2 − ( a q ) \ce{CO3^2-{}_{(aq)}} C O 3 2 − ( a q ) \ce{CO3^2-{}_{(aq)}} 
\ce{NaOH(aq,$\infty$)}
 Na O H ( aq , ∞ ) \ce{NaOH(aq,$\infty$)} Na O H ( aq , ∞ ) \ce{NaOH(aq,$\infty$)} 
\ce{OCO^{.-}}
 O C O • − \ce{OCO^{.-}} O C O • − \ce{OCO^{.-}} 
\ce{NO^{(2.)-}}
 N O ( 2 • ) − \ce{NO^{(2.)-}} N O ( 2 • ) − \ce{NO^{(2.)-}} 
\ce{NO_x}
 N O x \ce{NO_x} N O x \ce{NO_x} 
\ce{Fe^n+}
 Fe n + \ce{Fe^n+} Fe n + \ce{Fe^n+} 
\ce{x Na(NH4)HPO4 ->[\Delta] (NaPO3)_x + x NH3 ^ + x H2O}
 x Na ( N H 4 ) H P O 4 → Δ ( Na P O 3 ) x + x N H 3 ↑ + x H 2 O \ce{x Na(NH4)HPO4 ->[\Delta] (NaPO3)_x + x NH3 ^ + x H2O} x Na ( N H 4 ) H P O 4 → Δ ( Na P O 3 ) x + x N H 3 ↑ + x H 2 O \ce{x Na(NH4)HPO4 ->[\Delta] (NaPO3)_x + x NH3 ^ + x H2O} 
\ce{\mu-Cl}
 μ - Cl \ce{\mu-Cl} μ - Cl \ce{\mu-Cl} 
\ce{[Pt(\eta^2-C2H4)Cl3]-}
 [ Pt ( η 2 - C 2 H 4 ) Cl 3 ] − \ce{[Pt(\eta^2-C2H4)Cl3]-} [ Pt ( η 2 - C 2 H 4 ) Cl 3 ] − \ce{[Pt(\eta^2-C2H4)Cl3]-} 
\ce{^234_90Th -> ^0_-1\beta{} + ^234_91Pa}
 90 234 Th → − 1 0 β + 91 234 Pa \ce{^234_90Th -> ^0_-1\beta{} + ^234_91Pa} 90 234 Th → − 1 0 β + 91 234 Pa \ce{^234_90Th -> ^0_-1\beta{} + ^234_91Pa} 
\ce{Fe(CN)_{$\frac{6}{2}$}}
 Fe ( C N ) 6 2 \ce{Fe(CN)_{$\frac{6}{2}$}} Fe ( C N ) 6 2 \ce{Fe(CN)_{$\frac{6}{2}$}} 
\ce{NO_$x$}
 N O x \ce{NO_$x$} N O x \ce{NO_$x$} 
\ce{NO_${x}$}
 N O x \ce{NO_${x}$} N O x \ce{NO_${x}$} 
\ce{$cis${-}[PtCl2(NH3)2]}
 c i s - [ Pt Cl 2 ( N H 3 ) 2 ] \ce{$cis${-}[PtCl2(NH3)2]} c i s - [ Pt Cl 2 ( N H 3 ) 2 ] \ce{$cis${-}[PtCl2(NH3)2]} 
\ce{{(+)}_589{-}[Co(en)3]Cl3}
 (+) 589 - [ Co ( en ) 3 ] Cl 3 \ce{{(+)}_589{-}[Co(en)3]Cl3} (+) 589 - [ Co ( en ) 3 ] Cl 3 \ce{{(+)}_589{-}[Co(en)3]Cl3} 
\ce{KCr(SO4)2*12H2O}
 K Cr ( S O 4 ) 2 ⋅ H 2 O \ce{KCr(SO4)2*12H2O} K Cr ( S O 4 ) 2 ⋅ H 2 O \ce{KCr(SO4)2*12H2O} 
\ce{KCr(SO4)2.12H2O}
 K Cr ( S O 4 ) 2.12 H 2 O \ce{KCr(SO4)2.12H2O} K Cr ( S O 4 ) 2.12 H 2 O \ce{KCr(SO4)2.12H2O} 
\ce{KCr(SO4)2 * 12 H2O}
 K Cr ( S O 4 ) 2 ⋅ 12 H 2 O \ce{KCr(SO4)2 * 12 H2O} K Cr ( S O 4 ) 2 ⋅ 12 H 2 O \ce{KCr(SO4)2 * 12 H2O} 
\ce{C6H5-CHO}
 C 6 H 5 − C H O \ce{C6H5-CHO} C 6 H 5 − C H O \ce{C6H5-CHO} 
\ce{A-B=C#D}
 A − B = C ≡ D \ce{A-B=C#D} A − B = C ≡ D \ce{A-B=C#D} 
\ce{A\bond{-}B\bond{=}C\bond{#}D}
 A − B = C ≡ D \ce{A\bond{-}B\bond{=}C\bond{#}D} A − B = C ≡ D \ce{A\bond{-}B\bond{=}C\bond{#}D} 
\ce{A\bond{1}B\bond{2}C\bond{3}D}
 A − B = C ≡ D \ce{A\bond{1}B\bond{2}C\bond{3}D} A − B = C ≡ D \ce{A\bond{1}B\bond{2}C\bond{3}D} 
\ce{A\bond{~}B\bond{~-}C}
 A ⋅ ⋅ ⋅ B C \ce{A\bond{~}B\bond{~-}C} A ⋅ ⋅ ⋅ B C \ce{A\bond{~}B\bond{~-}C} 
\ce{A\bond{~--}B\bond{~=}C\bond{-~-}D}
 A B C D \ce{A\bond{~--}B\bond{~=}C\bond{-~-}D} A B C D \ce{A\bond{~--}B\bond{~=}C\bond{-~-}D} 
\ce{A\bond{...}B\bond{....}C}
 A ⋅ ⋅ ⋅ B ⋅ ⋅ ⋅ ⋅ C \ce{A\bond{...}B\bond{....}C} A ⋅ ⋅ ⋅ B ⋅ ⋅ ⋅ ⋅ C \ce{A\bond{...}B\bond{....}C} 
\ce{A\bond{->}B\bond{<-}C}
 A → B ← C \ce{A\bond{->}B\bond{<-}C} A → B ← C \ce{A\bond{->}B\bond{<-}C} 
\ce{A -> B}
 A → B \ce{A -> B} A → B \ce{A -> B} 
\ce{A <- B}
 A ← B \ce{A <- B} A ← B \ce{A <- B} 
\ce{A <-> B}
 A ↔ B \ce{A <-> B} A ↔ B \ce{A <-> B} 
\ce{A <--> B}
 A ⇄ B \ce{A <--> B} A ⇄ B \ce{A <--> B} 
\ce{A <=> B}
 A ⇌ B \ce{A <=> B} A ⇌ B \ce{A <=> B} 
\ce{A <=>> B}
 A ⇀ ↽ B \ce{A <=>> B} A ⇀ ↽ B \ce{A <=>> B} 
\ce{A <<=> B}
 A ⇀ ↽ B \ce{A <<=> B} A ⇀ ↽ B \ce{A <<=> B} 
\ce{A ->[H2O] B}
 A → H 2 O B \ce{A ->[H2O] B} A → H 2 O B \ce{A ->[H2O] B} 
\ce{A ->[{text above}][{text below}] B}
 A → text below text above B \ce{A ->[{text above}][{text below}] B} A → text below text above B \ce{A ->[{text above}][{text below}] B} 
\ce{A ->[$x$][$x_i$] B}
 A → x i x B \ce{A ->[$x$][$x_i$] B} A → x i x B \ce{A ->[$x$][$x_i$] B} 
\ce{A ->[${x}$] B}
 A → x B \ce{A ->[${x}$] B} A → x B \ce{A ->[${x}$] B} 
\ce{A + B}
 A + B \ce{A + B} A + B \ce{A + B} 
\ce{A - B}
 A − B \ce{A - B} A − B \ce{A - B} 
\ce{A = B}
 A = B \ce{A = B} A = B \ce{A = B} 
\ce{A \pm B}
 A ± B \ce{A \pm B} A ± B \ce{A \pm B} 
\ce{SO4^2- + Ba^2+ -> BaSO4 v}
 S O 4 2 − + Ba 2 + → Ba S O 4 ↓ \ce{SO4^2- + Ba^2+ -> BaSO4 v} S O 4 2 − + Ba 2 + → Ba S O 4 ↓ \ce{SO4^2- + Ba^2+ -> BaSO4 v} 
\ce{A v B (v) -> B ^ B (^)}
 A ↓ B ↓ → B ↑ B ↑ \ce{A v B (v) -> B ^ B (^)} A ↓ B ↓ → B ↑ B ↑ \ce{A v B (v) -> B ^ B (^)} 
\ce{Zn^2+ <=>[+ 2OH-][+ 2H+] \underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}} <=>[+ 2OH-][+ 2H+] \underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}}
 Zn 2 + ⇌ + 2 H + + 2 O H − Zn ( O H ) 2 ↓ amphoteres Hydroxid ⇌ + 2 H + + 2 O H − [ Zn ( O H ) 4 ] − 2 Hydroxozikat \ce{Zn^2+ <=>[+ 2OH-][+ 2H+] \underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}} <=>[+ 2OH-][+ 2H+] \underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}} Zn 2 + ⇌ + 2 H + + 2 O H − Zn ( O H ) 2 ↓ amphoteres Hydroxid ⇌ + 2 H + + 2 O H − [ Zn ( O H ) 4 ] − 2 Hydroxozikat \ce{Zn^2+ <=>[+ 2OH-][+ 2H+] \underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}} <=>[+ 2OH-][+ 2H+] \underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}} 
\ce{\frac{[Hg^2+][Hg]}{[Hg2^2+]}}
 [ Hg 2 + ] [ Hg ] [ Hg 2 2 + ] \ce{\frac{[Hg^2+][Hg]}{[Hg2^2+]}} [ Hg 2 + ] [ Hg ] [ Hg 2 2 + ] \ce{\frac{[Hg^2+][Hg]}{[Hg2^2+]}} 
\ce{Hg^2+ ->[I-] \underset{\mathrm{red}}{\ce{HgI2}} ->[I-] \underset{\mathrm{red}}{\ce{[Hg^{II}I4]^2-}}}
 Hg 2 + → I − Hg I 2 r e d → I − [ Hg I I I 4 ] − 2 r e d \ce{Hg^2+ ->[I-] \underset{\mathrm{red}}{\ce{HgI2}} ->[I-] \underset{\mathrm{red}}{\ce{[Hg^{II}I4]^2-}}} Hg 2 + → I − Hg I 2 r e d → I − [ Hg I I I 4 ] − 2 r e d \ce{Hg^2+ ->[I-] \underset{\mathrm{red}}{\ce{HgI2}} ->[I-] \underset{\mathrm{red}}{\ce{[Hg^{II}I4]^2-}}} 
\ce{N2}
 N 2 \ce{N2} N 2 \ce{N2} 
\ce{O2}
 O 2 \ce{O2} O 2 \ce{O2} 
\ce{CO2}
 C O 2 \ce{CO2} C O 2 \ce{CO2} 
\begin{align}\ce{RNO2 &<=>[+e] RNO2^{-.} \\ RNO2^{-.} &<=>[+e] RNO2^2-}\end{align}
 R N O 2 ⇌ + e R N O 2 − • R N O 2 − • ⇌ + e R N O 2 2 − \begin{align}\ce{RNO2 &<=>[+e] RNO2^{-.} \\ RNO2^{-.} &<=>[+e] RNO2^2-}\end{align} R N O 2 ⇌ + e R N O 2 − • R N O 2 − • ⇌ + e R N O 2 2 − \begin{align}\ce{RNO2 &<=>[+e] RNO2^{-.} \\ RNO2^{-.} &<=>[+e] RNO2^2-}\end{align}
TreeBlood intmath Test
\frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} \equiv 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }
 1 ( ϕ 5 − ϕ ) e 25 π ≡ 1 + e − 2 π 1 + e − 4 π 1 + e − 6 π 1 + e − 8 π 1 + ⋯ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} \equiv 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } } 1 ( ϕ 5 − ϕ ) e 25 π ≡ 1 + e − 2 π 1 + e − 4 π 1 + e − 6 π 1 + e − 8 π 1 + ⋯ \frac{1}{\Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{\frac25 \pi}} \equiv 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } } 
\left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right)
 ( ∑ k = 1 n a k b k ) 2 ≤ ( ∑ k = 1 n a k 2 ) ( ∑ k = 1 n b k 2 ) \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) ( ∑ k = 1 n a k b k ) 2 ≤ ( ∑ k = 1 n a k 2 ) ( ∑ k = 1 n b k 2 ) \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) 
\displaystyle\sum_{i=1}^{k+1}i
 ∑ i = 1 k + 1 i \displaystyle\sum_{i=1}^{k+1}i ∑ i = 1 k + 1 i \displaystyle\sum_{i=1}^{k+1}i 
\displaystyle= \left(\sum_{i=1}^{k}i\right) +(k+1)
 = ( ∑ i = 1 k i ) + ( k + 1 ) \displaystyle= \left(\sum_{i=1}^{k}i\right) +(k+1) = ( ∑ i = 1 k i ) + ( k + 1 ) \displaystyle= \left(\sum_{i=1}^{k}i\right) +(k+1) 
\displaystyle= \frac{k(k+1)}{2}+k+1
 = k ( k + 1 ) 2 + k + 1 \displaystyle= \frac{k(k+1)}{2}+k+1 = k ( k + 1 ) 2 + k + 1 \displaystyle= \frac{k(k+1)}{2}+k+1 
\displaystyle= \frac{k(k+1)+2(k+1)}{2}
 = k ( k + 1 ) + 2 ( k + 1 ) 2 \displaystyle= \frac{k(k+1)+2(k+1)}{2} = k ( k + 1 ) + 2 ( k + 1 ) 2 \displaystyle= \frac{k(k+1)+2(k+1)}{2} 
\displaystyle= \frac{(k+1)(k+2)}{2}
 = ( k + 1 ) ( k + 2 ) 2 \displaystyle= \frac{(k+1)(k+2)}{2} = ( k + 1 ) ( k + 2 ) 2 \displaystyle= \frac{(k+1)(k+2)}{2} 
\displaystyle= \frac{(k+1)((k+1)+1)}{2}
 = ( k + 1 ) ( ( k + 1 ) + 1 ) 2 \displaystyle= \frac{(k+1)((k+1)+1)}{2} = ( k + 1 ) ( ( k + 1 ) + 1 ) 2 \displaystyle= \frac{(k+1)((k+1)+1)}{2} 
\displaystyle\text{ for }\lvert q\rvert < 1.
  for  | q | < 1. \displaystyle\text{ for }\lvert q\rvert < 1.  for  | q | < 1. \displaystyle\text{ for }\lvert q\rvert < 1. 
= \displaystyle \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})},
 = ∏ j = 0 ∞ 1 ( 1 − q 5 j + 2 ) ( 1 − q 5 j + 3 ) , = \displaystyle \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, = ∏ j = 0 ∞ 1 ( 1 − q 5 j + 2 ) ( 1 − q 5 j + 3 ) , = \displaystyle \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, 
\displaystyle 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots
 1 + q 2 ( 1 − q ) + q 6 ( 1 − q ) ( 1 − q 2 ) + ⋯ \displaystyle 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots 1 + q 2 ( 1 − q ) + q 6 ( 1 − q ) ( 1 − q 2 ) + ⋯ \displaystyle 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots 
k_{n+1} = n^2 + k_n^2 - k_{n-1}
 k n + 1 = n 2 + k n 2 − k n − 1 k_{n+1} = n^2 + k_n^2 - k_{n-1} k n + 1 = n 2 + k n 2 − k n − 1 k_{n+1} = n^2 + k_n^2 - k_{n-1} 
\Gamma\ \Delta\ \Theta\ \Lambda\ \Xi\ \Pi\ \Sigma\ \Upsilon\ \Phi\ \Psi\ \Omega
 Γ Δ Θ Λ Ξ Π Σ Υ Φ Ψ Ω \Gamma\ \Delta\ \Theta\ \Lambda\ \Xi\ \Pi\ \Sigma\ \Upsilon\ \Phi\ \Psi\ \Omega Γ Δ Θ Λ Ξ Π Σ Υ Φ Ψ Ω \Gamma\ \Delta\ \Theta\ \Lambda\ \Xi\ \Pi\ \Sigma\ \Upsilon\ \Phi\ \Psi\ \Omega 
\omicron\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega\ \varepsilon\ \vartheta\ \varpi\ \varrho\ \varsigma\ \varphi
 ο π ρ σ τ υ ϕ χ ψ ω ε ϑ ϖ ϱ ς φ \omicron\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega\ \varepsilon\ \vartheta\ \varpi\ \varrho\ \varsigma\ \varphi ο π ρ σ τ υ ϕ χ ψ ω ε ϑ ϖ ϱ ς φ \omicron\ \pi\ \rho\ \sigma\ \tau\ \upsilon\ \phi\ \chi\ \psi\ \omega\ \varepsilon\ \vartheta\ \varpi\ \varrho\ \varsigma\ \varphi 
\alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi
 α β γ δ ϵ ζ η θ ι κ λ μ ν ξ \alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi α β γ δ ϵ ζ η θ ι κ λ μ ν ξ \alpha\ \beta\ \gamma\ \delta\ \epsilon\ \zeta\ \eta\ \theta\ \iota\ \kappa\ \lambda\ \mu\ \nu\ \xi 
\gets\ \to\ \leftarrow\ \rightarrow\ \uparrow\ \Uparrow\ \downarrow\ \Downarrow\ \updownarrow\ \Updownarrow
 ← → ← → ↑ ⇑ ↓ ⇓ ↕ ⇕ \gets\ \to\ \leftarrow\ \rightarrow\ \uparrow\ \Uparrow\ \downarrow\ \Downarrow\ \updownarrow\ \Updownarrow ← → ← → ↑ ⇑ ↓ ⇓ ↕ ⇕ \gets\ \to\ \leftarrow\ \rightarrow\ \uparrow\ \Uparrow\ \downarrow\ \Downarrow\ \updownarrow\ \Updownarrow 
\Leftarrow\ \Rightarrow\ \leftrightarrow\ \Leftrightarrow\ \mapsto\ \hookleftarrow
 ⇐ ⇒ ↔ ⇔ ↦ ↩ \Leftarrow\ \Rightarrow\ \leftrightarrow\ \Leftrightarrow\ \mapsto\ \hookleftarrow ⇐ ⇒ ↔ ⇔ ↦ ↩ \Leftarrow\ \Rightarrow\ \leftrightarrow\ \Leftrightarrow\ \mapsto\ \hookleftarrow 
\leftharpoonup\ \leftharpoondown\ \rightleftharpoons\ \longleftarrow\ \Longleftarrow\ \longrightarrow
 ↼ ↽ ⇌ ⟵ ⟸ ⟶ \leftharpoonup\ \leftharpoondown\ \rightleftharpoons\ \longleftarrow\ \Longleftarrow\ \longrightarrow ↼ ↽ ⇌ ⟵ ⟸ ⟶ \leftharpoonup\ \leftharpoondown\ \rightleftharpoons\ \longleftarrow\ \Longleftarrow\ \longrightarrow 
\Longrightarrow\ \longleftrightarrow\ \Longleftrightarrow\ \longmapsto\ \hookrightarrow\ \rightharpoonup
 ⟹ ⟷ ⟺ ⟼ ↪ ⇀ \Longrightarrow\ \longleftrightarrow\ \Longleftrightarrow\ \longmapsto\ \hookrightarrow\ \rightharpoonup ⟹ ⟷ ⟺ ⟼ ↪ ⇀ \Longrightarrow\ \longleftrightarrow\ \Longleftrightarrow\ \longmapsto\ \hookrightarrow\ \rightharpoonup 
\rightharpoondown\ \leadsto\ \nearrow\ \searrow\ \swarrow\ \nwarrow
 ⇁ ⇝ ↗ ↘ ↙ ↖ \rightharpoondown\ \leadsto\ \nearrow\ \searrow\ \swarrow\ \nwarrow ⇁ ⇝ ↗ ↘ ↙ ↖ \rightharpoondown\ \leadsto\ \nearrow\ \searrow\ \swarrow\ \nwarrow 
\surd\ \barwedge\ \veebar\ \odot\ \oplus\ \otimes\ \oslash\ \circledcirc\ \boxdot\ \bigtriangleup
 √ ⌅ ⊻ ⊙ ⊕ ⊗ ⊘ ⊚ ⊡ △ \surd\ \barwedge\ \veebar\ \odot\ \oplus\ \otimes\ \oslash\ \circledcirc\ \boxdot\ \bigtriangleup √ ⌅ ⊻ ⊙ ⊕ ⊗ ⊘ ⊚ ⊡ △ \surd\ \barwedge\ \veebar\ \odot\ \oplus\ \otimes\ \oslash\ \circledcirc\ \boxdot\ \bigtriangleup 
\bigtriangledown\ \dagger\ \diamond\ \star\ \triangleleft\ \triangleright\ \angle\ \infty\ \prime\ \triangle
 ▽ † ⋄ ⋆ ◃ ▹ ∠ ∞ ′ △ \bigtriangledown\ \dagger\ \diamond\ \star\ \triangleleft\ \triangleright\ \angle\ \infty\ \prime\ \triangle ▽ † ⋄ ⋆ ◃ ▹ ∠ ∞ ′ △ \bigtriangledown\ \dagger\ \diamond\ \star\ \triangleleft\ \triangleright\ \angle\ \infty\ \prime\ \triangle 
\int u \frac{dv}{dx}\,dx=uv-\int \frac{du}{dx}v\,dx
 ∫ u d v d x d x = u v − ∫ d u d x v d x \int u \frac{dv}{dx}\,dx=uv-\int \frac{du}{dx}v\,dx ∫ u d v d x d x = u v − ∫ d u d x v d x \int u \frac{dv}{dx}\,dx=uv-\int \frac{du}{dx}v\,dx 
f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x}
 f ( x ) = ∫ − ∞ ∞ f ^ ( ξ ) e 2 π i ξ x f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x} f ( x ) = ∫ − ∞ ∞ f ^ ( ξ ) e 2 π i ξ x f(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x} 
\oint \vec{F} \cdot d\vec{s}=0
 ∮ F ⃗ ⋅ d s ⃗ = 0 \oint \vec{F} \cdot d\vec{s}=0 ∮ F ⃗ ⋅ d s ⃗ = 0 \oint \vec{F} \cdot d\vec{s}=0 
\begin{aligned}\dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy\end{aligned}
 x ˙ = σ ( y − x ) y ˙ = ρ x − y − x z z ˙ = − β z + x y \begin{aligned}\dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy\end{aligned} x ˙ = σ ( y − x ) y ˙ = ρ x − y − x z z ˙ = − β z + x y \begin{aligned}\dot{x} & = \sigma(y-x) \\ \dot{y} & = \rho x - y - xz \\ \dot{z} & = -\beta z + xy\end{aligned} 
\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}\mathbf{i} & \mathbf{j} & \mathbf{k} \\\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0\end{vmatrix}
 𝐕 1 × 𝐕 2 = | 𝐢 𝐣 𝐤 ∂ X ∂ u ∂ Y ∂ u 0 ∂ X ∂ v ∂ Y ∂ v 0 | \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}\mathbf{i} & \mathbf{j} & \mathbf{k} \\\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0\end{vmatrix} 𝐕 1 × 𝐕 2 = | 𝐢 𝐣 𝐤 ∂ X ∂ u ∂ Y ∂ u 0 ∂ X ∂ v ∂ Y ∂ v 0 | \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}\mathbf{i} & \mathbf{j} & \mathbf{k} \\\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0\end{vmatrix} 
\mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}\mathbf{i} & \mathbf{j} & \mathbf{k} \\\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0\end{vmatrix}
 𝐕 1 × 𝐕 2 = | 𝐢 𝐣 𝐤 ∂ X ∂ u ∂ Y ∂ u 0 ∂ X ∂ v ∂ Y ∂ v 0 | \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}\mathbf{i} & \mathbf{j} & \mathbf{k} \\\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0\end{vmatrix} 𝐕 1 × 𝐕 2 = | 𝐢 𝐣 𝐤 ∂ X ∂ u ∂ Y ∂ u 0 ∂ X ∂ v ∂ Y ∂ v 0 | \mathbf{V}_1 \times \mathbf{V}_2 = \begin{vmatrix}\mathbf{i} & \mathbf{j} & \mathbf{k} \\\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0\end{vmatrix} 
\hat{x}\ \vec{x}\ \ddot{x}
 x ^ x ⃗ x ̈ \hat{x}\ \vec{x}\ \ddot{x} x ^ x ⃗ x ̈ \hat{x}\ \vec{x}\ \ddot{x} 
\left(\frac{x^2}{y^3}\right)
 ( x 2 y 3 ) \left(\frac{x^2}{y^3}\right) ( x 2 y 3 ) \left(\frac{x^2}{y^3}\right) 
\left.\frac{x^3}{3}\right|_0^1
 x 3 3 | 0 1 \left.\frac{x^3}{3}\right|_0^1 x 3 3 | 0 1 \left.\frac{x^3}{3}\right|_0^1 
f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\ 3n+1, & \text{if } n\text{ is odd} \end{cases}
 f ( n ) = { n 2 , if  n  is even 3 n + 1 , if  n  is odd f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\ 3n+1, & \text{if } n\text{ is odd} \end{cases} f ( n ) = { n 2 , if  n  is even 3 n + 1 , if  n  is odd f(n) = \begin{cases} \frac{n}{2}, & \text{if } n\text{ is even} \\ 3n+1, & \text{if } n\text{ is odd} \end{cases} 
\begin{aligned}\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
 ∇ × 𝐁 ⃗ − 1 c ∂ 𝐄 ⃗ ∂ t = 4 π c 𝐣 ⃗ ∇ ⋅ 𝐄 ⃗ = 4 π ρ ∇ × 𝐄 ⃗ + 1 c ∂ 𝐁 ⃗ ∂ t = 𝟎 ⃗ ∇ ⋅ 𝐁 ⃗ = 0 \begin{aligned}\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} ∇ × 𝐁 ⃗ − 1 c ∂ 𝐄 ⃗ ∂ t = 4 π c 𝐣 ⃗ ∇ ⋅ 𝐄 ⃗ = 4 π ρ ∇ × 𝐄 ⃗ + 1 c ∂ 𝐁 ⃗ ∂ t = 𝟎 ⃗ ∇ ⋅ 𝐁 ⃗ = 0 \begin{aligned}\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} 
\begin{aligned}\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\[1em] \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\[0.5em]\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\[1em]\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
 ∇ × 𝐁 ⃗ − 1 c ∂ 𝐄 ⃗ ∂ t = 4 π c 𝐣 ⃗ ∇ ⋅ 𝐄 ⃗ = 4 π ρ ∇ × 𝐄 ⃗ + 1 c ∂ 𝐁 ⃗ ∂ t = 𝟎 ⃗ ∇ ⋅ 𝐁 ⃗ = 0 \begin{aligned}\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\[1em] \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\[0.5em]\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\[1em]\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} ∇ × 𝐁 ⃗ − 1 c ∂ 𝐄 ⃗ ∂ t = 4 π c 𝐣 ⃗ ∇ ⋅ 𝐄 ⃗ = 4 π ρ ∇ × 𝐄 ⃗ + 1 c ∂ 𝐁 ⃗ ∂ t = 𝟎 ⃗ ∇ ⋅ 𝐁 ⃗ = 0 \begin{aligned}\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\[1em] \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\[0.5em]\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\[1em]\nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} 
\frac{n!}{k!(n-k)!} = {^n}C_k
 n ! k ! ( n − k ) ! = n C k \frac{n!}{k!(n-k)!} = {^n}C_k n ! k ! ( n − k ) ! = n C k \frac{n!}{k!(n-k)!} = {^n}C_k 
n \choose k
 ( n k ) n \choose k ( n k ) n \choose k 
\frac{\frac{1}{x}+\frac{1}{y}}{y-z}
 1 x + 1 y y − z \frac{\frac{1}{x}+\frac{1}{y}}{y-z} 1 x + 1 y y − z \frac{\frac{1}{x}+\frac{1}{y}}{y-z} 
\sqrt[n]{1+x+x^2+x^3+\ldots}
 1 + x + x 2 + x 3 + … n \sqrt[n]{1+x+x^2+x^3+\ldots} 1 + x + x 2 + x 3 + … n \sqrt[n]{1+x+x^2+x^3+\ldots} 
\begin{pmatrix}a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\end{pmatrix}
 ( a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ) \begin{pmatrix}a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\end{pmatrix} ( a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ) \begin{pmatrix}a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\end{pmatrix} 
\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix}
 [ 0 ⋯ 0 ⋮ ⋱ ⋮ 0 ⋯ 0 ] \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix} [ 0 ⋯ 0 ⋮ ⋱ ⋮ 0 ⋯ 0 ] \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0 \end{bmatrix} 
f(x) = \sqrt{1+x} \quad (x \ge -1)
 f ( x ) = 1 + x ( x ≥ − 1 ) f(x) = \sqrt{1+x} \quad (x \ge -1) f ( x ) = 1 + x ( x ≥ − 1 ) f(x) = \sqrt{1+x} \quad (x \ge -1) 
f(x) \sim x^2 \quad (x\to\infty)
 f ( x ) ∼ x 2 ( x → ∞ ) f(x) \sim x^2 \quad (x\to\infty) f ( x ) ∼ x 2 ( x → ∞ ) f(x) \sim x^2 \quad (x\to\infty) 
f(x) = \sqrt{1+x}, \quad x \ge -1
 f ( x ) = 1 + x , x ≥ − 1 f(x) = \sqrt{1+x}, \quad x \ge -1 f ( x ) = 1 + x , x ≥ − 1 f(x) = \sqrt{1+x}, \quad x \ge -1 
f(x) \sim x^2, \quad x\to\infty
 f ( x ) ∼ x 2 , x → ∞ f(x) \sim x^2, \quad x\to\infty f ( x ) ∼ x 2 , x → ∞ f(x) \sim x^2, \quad x\to\infty 
\mathcal L_{\mathcal T}(\vec{\lambda}) = \sum_{(\mathbf{x},\mathbf{s})\in \mathcal T} \log P(\mathbf{s}\mid\mathbf{x}) - \sum_{i=1}^m \frac{\lambda_i^2}{2\sigma^2}
 ℒ︀ 𝒯︀ ( λ ⃗ ) = ∑ ( 𝐱 , 𝐬 ) ∈ 𝒯︀ log P ( 𝐬 ∣ 𝐱 ) − ∑ i = 1 m λ i 2 2 σ 2 \mathcal L_{\mathcal T}(\vec{\lambda}) = \sum_{(\mathbf{x},\mathbf{s})\in \mathcal T} \log P(\mathbf{s}\mid\mathbf{x}) - \sum_{i=1}^m \frac{\lambda_i^2}{2\sigma^2} ℒ︀ 𝒯︀ ( λ ⃗ ) = ∑ ( 𝐱 , 𝐬 ) ∈ 𝒯︀ log P ( 𝐬 ∣ 𝐱 ) − ∑ i = 1 m λ i 2 2 σ 2 \mathcal L_{\mathcal T}(\vec{\lambda}) = \sum_{(\mathbf{x},\mathbf{s})\in \mathcal T} \log P(\mathbf{s}\mid\mathbf{x}) - \sum_{i=1}^m \frac{\lambda_i^2}{2\sigma^2} 
S (\omega)=\frac{\alpha g^2}{\omega^5} \,e ^{[-0.74\bigl\{\frac{\omega U_\omega 19.5}{g}\bigr\}^{-4}]}
 S ( ω ) = α g 2 ω 5 e [ − 0.74 { ω U ω 19.5 g } − 4 ] S (\omega)=\frac{\alpha g^2}{\omega^5} \,e ^{[-0.74\bigl\{\frac{\omega U_\omega 19.5}{g}\bigr\}^{-4}]} S ( ω ) = α g 2 ω 5 e [ − 0.74 { ω U ω 19.5 g } − 4 ] S (\omega)=\frac{\alpha g^2}{\omega^5} \,e ^{[-0.74\bigl\{\frac{\omega U_\omega 19.5}{g}\bigr\}^{-4}]}
TreeBlood limits Test
\sigma = \sqrt{\frac 1 n \sum_{i=1}^n (\mu - x_i)^2}
 σ = 1 n ∑ i = 1 n ( μ − x i ) 2 \sigma = \sqrt{\frac 1 n \sum_{i=1}^n (\mu - x_i)^2} σ = 1 n ∑ i = 1 n ( μ − x i ) 2 \sigma = \sqrt{\frac 1 n \sum_{i=1}^n (\mu - x_i)^2} 
\left.\int_a^b f(x) dx =  F(x) \right\mid_a^b
 ∫ a b f ( x ) d x = F ( x ) ∣ a b \left.\int_a^b f(x) dx = F(x) \right\mid_a^b ∫ a b f ( x ) d x = F ( x ) ∣ a b \left.\int_a^b f(x) dx = F(x) \right\mid_a^b 
\lim_{b\to\infty}\int_0^{b}e^{-x^2} dx = \frac{\sqrt{\pi}}{2}
 lim b → ∞ ∫ 0 b e − x 2 d x = π 2 \lim_{b\to\infty}\int_0^{b}e^{-x^2} dx = \frac{\sqrt{\pi}}{2} lim b → ∞ ∫ 0 b e − x 2 d x = π 2 \lim_{b\to\infty}\int_0^{b}e^{-x^2} dx = \frac{\sqrt{\pi}}{2} 
\int_{\int_a^b f(x) dx}^{\int_c^d g(x) dx}h(x)dx
 ∫ ∫ a b f ( x ) d x ∫ c d g ( x ) d x h ( x ) d x \int_{\int_a^b f(x) dx}^{\int_c^d g(x) dx}h(x)dx ∫ ∫ a b f ( x ) d x ∫ c d g ( x ) d x h ( x ) d x \int_{\int_a^b f(x) dx}^{\int_c^d g(x) dx}h(x)dx 
\Gamma(t) = \int_0^{+\infty} x^{t-1}e^{-x}\dv*{x}!/ = \frac 1 t \prod_{n=1}^{\infty}\frac{(1+\frac 1 t)^t}{1+\frac 1 t} \sim\sqrt{\frac{2\pi}{t}}{\left(\frac t e \right)^t}
 Γ ( t ) = ∫ 0 + ∞ x t − 1 e − x dv x ! / = 1 t ∏ n = 1 ∞ ( 1 + 1 t ) t 1 + 1 t ∼ 2 π t ( t e ) t \Gamma(t) = \int_0^{+\infty} x^{t-1}e^{-x}\dv*{x}!/ = \frac 1 t \prod_{n=1}^{\infty}\frac{(1+\frac 1 t)^t}{1+\frac 1 t} \sim\sqrt{\frac{2\pi}{t}}{\left(\frac t e \right)^t} Γ ( t ) = ∫ 0 + ∞ x t − 1 e − x dv x ! / = 1 t ∏ n = 1 ∞ ( 1 + 1 t ) t 1 + 1 t ∼ 2 π t ( t e ) t \Gamma(t) = \int_0^{+\infty} x^{t-1}e^{-x}\dv*{x}!/ = \frac 1 t \prod_{n=1}^{\infty}\frac{(1+\frac 1 t)^t}{1+\frac 1 t} \sim\sqrt{\frac{2\pi}{t}}{\left(\frac t e \right)^t} 
\int_0^1 x^x\,\mathrm{d}x = \sum_{n = 1}^\infty{(-1)^{n + 1}\,n^{-n}}
 ∫ 0 1 x x d x = ∑ n = 1 ∞ ( − 1 ) n + 1 n − n \int_0^1 x^x\,\mathrm{d}x = \sum_{n = 1}^\infty{(-1)^{n + 1}\,n^{-n}} ∫ 0 1 x x d x = ∑ n = 1 ∞ ( − 1 ) n + 1 n − n \int_0^1 x^x\,\mathrm{d}x = \sum_{n = 1}^\infty{(-1)^{n + 1}\,n^{-n}} 
\sideset{_{{}_\alpha^\beta\mathfrak{A}_\delta^\gamma}^{{}_\epsilon^\zeta\mathfrak{B}_\theta^\eta}}{_{{}_\rho^\sigma\mathfrak{E}_\upsilon^\tau}^{{}_\nu^\xi\mathfrak{D}_\pi^o}}\prod_{{}_\phi^\chi\mathfrak{F}_\omega^\psi}^{{}_\iota^\kappa\mathfrak{C}_\mu^\lambda}
 ∏ ρ σ 𝔈 υ τ ν ξ 𝔇 π o α β 𝔄 δ γ ϵ ζ 𝔅 θ η ϕ χ 𝔉 ω ψ ι κ ℭ μ λ \sideset{_{{}_\alpha^\beta\mathfrak{A}_\delta^\gamma}^{{}_\epsilon^\zeta\mathfrak{B}_\theta^\eta}}{_{{}_\rho^\sigma\mathfrak{E}_\upsilon^\tau}^{{}_\nu^\xi\mathfrak{D}_\pi^o}}\prod_{{}_\phi^\chi\mathfrak{F}_\omega^\psi}^{{}_\iota^\kappa\mathfrak{C}_\mu^\lambda} ∏ ρ σ 𝔈 υ τ ν ξ 𝔇 π o α β 𝔄 δ γ ϵ ζ 𝔅 θ η ϕ χ 𝔉 ω ψ ι κ ℭ μ λ \sideset{_{{}_\alpha^\beta\mathfrak{A}_\delta^\gamma}^{{}_\epsilon^\zeta\mathfrak{B}_\theta^\eta}}{_{{}_\rho^\sigma\mathfrak{E}_\upsilon^\tau}^{{}_\nu^\xi\mathfrak{D}_\pi^o}}\prod_{{}_\phi^\chi\mathfrak{F}_\omega^\psi}^{{}_\iota^\kappa\mathfrak{C}_\mu^\lambda} 
\sum_{\substack{1\lt i\lt 3 \\ 1\le j\lt 5}}a_{ij}=\prod^{\substack{1\lt i\lt 3 \\ 1\le j\lt 5}}b_{ij}
 ∑ 1 < i < 3 1 ≤ j < 5 a i j = ∏ 1 < i < 3 1 ≤ j < 5 b i j \sum_{\substack{1\lt i\lt 3 \\ 1\le j\lt 5}}a_{ij}=\prod^{\substack{1\lt i\lt 3 \\ 1\le j\lt 5}}b_{ij} ∑ 1 < i < 3 1 ≤ j < 5 a i j = ∏ 1 < i < 3 1 ≤ j < 5 b i j \sum_{\substack{1\lt i\lt 3 \\ 1\le j\lt 5}}a_{ij}=\prod^{\substack{1\lt i\lt 3 \\ 1\le j\lt 5}}b_{ij} 
\lim_{x\to a} \quad \int_a^b f(x) dx \quad \sum_{i=0}^n a_i
 lim x → a ∫ a b f ( x ) d x ∑ i = 0 n a i \lim_{x\to a} \quad \int_a^b f(x) dx \quad \sum_{i=0}^n a_i lim x → a ∫ a b f ( x ) d x ∑ i = 0 n a i \lim_{x\to a} \quad \int_a^b f(x) dx \quad \sum_{i=0}^n a_i 
\lim\limits_{x\to a} \quad \int\limits_a^b f(x) dx \quad \sum\limits_{i=0}^n a_i
 lim x → a ∫ a b f ( x ) d x ∑ i = 0 n a i \lim\limits_{x\to a} \quad \int\limits_a^b f(x) dx \quad \sum\limits_{i=0}^n a_i lim x → a ∫ a b f ( x ) d x ∑ i = 0 n a i \lim\limits_{x\to a} \quad \int\limits_a^b f(x) dx \quad \sum\limits_{i=0}^n a_i 
\lim\nolimits_{x\to a} \quad \int\nolimits_a^b f(x) dx \quad \sum\nolimits_{i=0}^n a_i
lim x → a ∫ a b f ( x ) d x ∑ i = 0 n a i \lim\nolimits_{x\to a} \quad \int\nolimits_a^b f(x) dx \quad \sum\nolimits_{i=0}^n a_i lim x → a ∫ a b f ( x ) d x ∑ i = 0 n a i \lim\nolimits_{x\to a} \quad \int\nolimits_a^b f(x) dx \quad \sum\nolimits_{i=0}^n a_i
TreeBlood scripts Test
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x^{\text{hello world}}
x hello world x^{\text{hello world}} x hello world x^{\text{hello world}}