ghost markdown 数学公式
Inline equation: $equation$
Inline equation: $equation$
Operators
$x + y$
- $x + y$
$x - y$
- $x - y$
$x \times y$
- $x \times y$
$x \div y$
- $x \div y$
$\dfrac{x}{y}$
- $\dfrac{x}{y}$
$\sqrt{x}$
- $\sqrt{x}$
Symbols
$\pi \approx 3.14159$
- $\pi \approx 3.14159$
$\pm 0.2$
- $\pm 0.2$
$\dfrac{0}{1} \neq \infty$
- $\dfrac{0}{1} \neq \infty$
$0 < x < 1$
- $0 < x < 1$
$0 \leq x \leq 1$
- $0 \leq x \leq 1$
$x \geq 10$
- $x \geq 10$
$\forall \, x \in (1,2)$
- $\forall , x \in (1,2)$
$\exists \, x \notin [0,1]$
- $\exists , x \notin [0,1]$
$A \subset B$
- $A \subset B$
$A \subseteq B$
- $A \subseteq B$
$A \cup B$
- $A \cup B$
$A \cap B$
- $A \cap B$
$X \implies Y$
- $X \implies Y$
$X \impliedby Y$
- $X \impliedby Y$
$a \to b$
- $a \to b$
$a \longrightarrow b$
- $a \longrightarrow b$
$a \Rightarrow b$
- $a \Rightarrow b$
$a \Longrightarrow b$
- $a \Longrightarrow b$
$a \propto b$
- $a \propto b$
$\bar a$
- $\bar a$
$\tilde a$
- $\tilde a$
$\breve a$
- $\breve a$
$\hat a$
- $\hat a$
$a^ \prime$
- $a^ \prime$
$a^ \dagger$
- $a^ \dagger$
$a^ \ast$
- $a^ \ast$
$a^ \star$
- $a^ \star$
$\mathcal A$
- $\mathcal A$
$\mathrm a$
- $\mathrm a$
$\cdots$
- $\cdots$
$\vdots$
- $\vdots$
$\#$
- $#$
$\$$
- $$$
$\%$
- $%$
$\&$
- $&$
$\{ \}$
- ${ }$
$\_$
- $_$
Space
- Horizontal space:
\quad - Large horizontal space:
\qquad - Small space:
\, - Medium space:
\: - Large space:
\; - Negative space:
\!
start a new line \\
<div>
$$
\begin{align}
A \\ B
\end{align}
$$
</div>
Greek alphabets
| Small Letter | Capital Letter | Alternative |
|---|---|---|
$\alpha$ \alpha |
A A |
|
$\beta$ \beta |
B B |
|
$\gamma$ \gamma |
Γ \Gamma |
|
$\delta$ \delta |
Δ \Delta |
|
$\epsilon$ \epsilon |
E E |
ε \varepsilon |
$\zeta$ \zeta |
Z Z |
|
$\eta$ \eta |
H H |
|
$\theta$ \theta |
Θ \Theta |
ϑ \vartheta |
$\zeta$ \zeta |
I I |
|
$\kappa$ \kappa |
K K |
ϰ \varkappa |
$\lambda$ \lambda |
Λ \Lambda |
|
$\mu$ \mu |
M M |
|
$\nu$ \nu |
N N |
|
$\xi$ \xi |
Ξ \Xi |
|
$\omicron$ \omicron |
O O |
|
$\pi$ \pi |
Π \Pi |
ϖ \varpi |
$\rho$ \rho |
P P |
ϱ \varrho |
$\sigma$ \sigma |
Σ \Sigma |
ς \varsigma |
$\tau$ \tau |
T T |
|
$\upsilon$ \upsilon |
Υ \Upsilon |
|
$\phi$ \phi |
Φ \Phi |
φ \varphi |
$\chi$ \chi |
X X |
|
$\psi$ \psi |
Ψ \Psi |
|
$\omega$ \omega |
Ω \Omega |
Equations
$$\mathbb{N} = { a \in \mathbb{Z} : a > 0 }$$
$$\mathbb{N} = \{ a \in \mathbb{Z} : a > 0 \}$$
$$\forall ; x \in X \quad \exists ; y \leq \epsilon$$
$$\forall \; x \in X \quad \exists \; y \leq \epsilon$$
$$\color{blue}{X \sim Normal ; (\mu,\sigma^2)}$$
$$\color{blue}{X \sim Normal \; (\mu,\sigma^2)}$$
$$P \left( A=2 , \middle| , \dfrac{A^2}{B}>4 \right)$$
$$P \left( A=2 \, \middle| \, \dfrac{A^2}{B}>4 \right)$$
$$f(x) = x^2 - x^\frac{1}{\pi}$$
$$f(x) = x^2 - x^\frac{1}{\pi}$$
$$f(X,n) = X_n + X_{n-1}$$
$$f(X,n) = X_n + X_{n-1}$$
$$f(x) = \sqrt[3]{2x} + \sqrt{x-2}$$
$$f(x) = \sqrt[3]{2x} + \sqrt{x-2}$$
$$\mathrm{e} = \sum_{n=0}^{\infty} \dfrac{1}{n!}$$
$$\mathrm{e} = \sum_{n=0}^{\infty} \dfrac{1}{n!}$$
$$\prod_{i=1}^{n} x_i - 1$$
$$\prod_{i=1}^{n} x_i - 1$$
$$\lim_{x \to 0^+} \dfrac{1}{x} = \infty$$
$$\lim_{x \to 0^+} \dfrac{1}{x} = \infty$$
$$\int_a^b y : \mathrm{d}x$$
$$\int_a^b y \: \mathrm{d}x$$
$$\log_a b = 1$$
$$\log_a b = 1$$
$$\max(S) = \max_{i:S_i \in S} S_i$$
$$\max(S) = \max_{i:S_i \in S} S_i$$
$$\frac{n!}{k!(n-k)!} = \binom{n}{k}$$
$$\frac{n!}{k!(n-k)!} = \binom{n}{k}$$
$$\text{$\dfrac{b}{a+b}=3, :$ therefore we can set $: a=6$}$$
$$\text{$\dfrac{b}{a+b}=3, \:$ therefore we can set $\: a=6$}$$
Functions
<div>
$$
f(x)=
\begin{cases}
1/d_{ij} & \quad \text{when $d_{ij} \leq 160$}\\
0 & \quad \text{otherwise}
\end{cases}
$$
</div>
Matrices
<div>
$$
\begin{matrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{matrix}
$$
</div>
<div>
$$
M =
\begin{bmatrix}
\frac{5}{6} & \frac{1}{6} & 0 \\[0.3em]
\frac{5}{6} & 0 & \frac{1}{6} \\[0.3em]
0 & \frac{5}{6} & \frac{1}{6}
\end{bmatrix}
$$
</div>
<div>
$$
M =
\begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}
\begin{bmatrix}
1 & 0 \\
0 & 1
\end{bmatrix}
$$
</div>
<div>
$$
M =
\begin{pmatrix}
1 & 0 \\
0 & 1
\end{pmatrix}
\begin{pmatrix}
1 & 0 \\
0 & 1
\end{pmatrix}
$$
</div>
<div>
$$
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}
$$
</div>