markdown中数学符号公式和字母表示_markdown 约等于

一. 常用数学符号markdown表示

• 乘号，正负号，：$\times$ $\pm$: $\times$ $\pm$
• 除号， 竖线：$\div$ $\mid$: $÷$ $\mid$
• 点：$\cdot$: $\cdot$
• 圆$\circ$: $\circ$
• 克罗内克积$\bigotimes$: $⨂$
• 异或$\bigoplus$: $⨁$
• 小于等于，大于等于 不等于$\leq$ $\geq$ $\neq$: $\le$ $\ge$ $\ne$
• 约等于$\approx$: $\approx$
• 积分，双重积分，曲线积分$\int$ $\iint$ $\oint$: $\int$ $\iint$ $\oint$
• 无穷$\infty$: $\infty$
• 梯度$\nabla$: $\nabla$
• 因为，所以$\because$ 和 $\therefore$ $\because$ 和 $\therefore$
• 任意和存在$\forall$ 和 $\exists$: $\forall$ 和 $\exists$
• 属于和不属于$\in$ 和 $\notin$: $\in$ 和 $\notin$
• 子集，真子集，空集$\subset$，$\subseteq$，$\emptyset$: $\subset$，$\subseteq$，$\varnothing$
• 交集和并集$\bigcap$ 和 $\bigcup$:$\bigcap$ 和 $\bigcup$
• 逻辑或 和 逻辑与$\bigvee$ 和 $\bigwedge$: $\bigvee$ 和 $\bigwedge$
• 期望值$\hat{y}$: $\hat{y}$
• 平均值$\overline{a+b+c+d}$: $\overline{a+b+c+d}$

二. 数学符号markdown表示的案例

三角函数：$$\sin$$: $$\sin$$

分数:

• $\dfrac{2}{3}$，$\tfrac{2}{3}$: $\frac{2}{3}$，$\frac{2}{3}$
• $$\frac{7x+5}{2+y^2}$$ 效果为：$$\frac{7x+5}{2+y^2}$$
• $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$: $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$

对数函数： $$\ln15, \log_2 10 , \lg7$$: $$\ln 15,{\log }_{2}10,\lg 7$$

关系运算符: $$\pm \times \div \sum \prod \neq \leq \geq$$: $$\pm \times ÷\sum \prod \ne \le \ge$$

---

上标：

• $A^2$、$A^{上标}$ : $A^2$、$A^{上标}$
• $$A^2 \; A^{上标} \; \mathop{A}\limits^2$$ $$A^2{A}^{上标}\stackrel{2}{A}$$

---

下标:

• $A_2$、$A_{下标}$ $A_2$、$A_{下标}$
• $$A_2 \; A_{下标}\; \mathop{A}\limits_2$$: $$A_2{A}_{下标}\underset{2}{A}$$
• $$z=z_l$$: $$z=z_l$$

---

开根号:

• $\sqrt[开方数]{参数}$ : $\sqrt[开方数]{参数}$
• $$\sqrt[开方数]{参数}$$: $$\sqrt[开方数]{参数}$$
• $$\sqrt{2};\sqrt[n]{3}$$: $$\sqrt{2};\sqrt[n]{3}$$
• $$ \sqrt x * \sqrt[3] x * \sqrt[-1] x $$: $$\sqrt{x}\ast \sqrt[3]{x}\ast \sqrt[-1]{x}$$

---

求和:

• $\sum$: $\sum$
• 求和上下标：$\sum_{i=0}^n$: ${\sum }_{i=0}^n$
• $$\sum ^2_3\;\sum \nolimits^2_3$$ : $$\sum _3^2{\sum }_3^2$$

---

积分:

• $\int$: $\int$
• $$\int ^2_3\;\int \limits^2_3$$: $${\int }_3^2\underset{3}{\overset{2}{\int }}$$
• $$\int ^2_3 x^2 {\rm d}x$$: $${\int }_3^2{x}^2\mathrm{d}x$$
• $$\iint$$: $$\iint$$

---

极限：

• $$\lim_{n\rightarrow+\infty} n$$: $$\underset{n\to +\infty }{\lim }n$$
• $$\begin{aligned} \lim_{a\to \infty} \tfrac{1}{a} \end{aligned}$$: $$\begin{array}{r}\underset{a\to \infty }{\lim }\frac{1}{a}\end{array}$$

---

累加：$$\sum \frac{1}{i^2}$$: $$\sum \frac{1}{i^2}$$
累乘：

• $$\prod \frac{1}{i^2}$$: $$\prod \frac{1}{i^2}$$
• $$ \prod_{{ \begin{gathered} 1\le i \le n\\ 1\le j \le m \end{gathered} }} M_{i,j} $$:
  $$\prod _{\begin{array}{c}1\le i\le n\\ 1\le j\le m\end{array}}{M}_{i,j}$$

---

矢量：$$\vec{a} \cdot \vec{b}=0$$: $$$\vec{a}\cdot \vec{b}=0$

三. 希腊字符

$$\alpha \beta \gamma \delta \epsilon $$: $$\alpha \beta \gamma \delta ϵ$$
$$ \zeta \eta \theta \vartheta \iota $$: $$\zeta \eta \theta \vartheta \iota$$
$$ \kappa \lambda \mu \nu \xi $$: $$\kappa \lambda \mu \nu \xi$$
$$o \pi \varpi \rho \varrho $$: $$o\pi \varpi \rho \varrho$$
$$ \sigma \varsigma \tau \upsilon \phi $$: $$\sigma \varsigma \tau \upsilon \varphi$$
$$ \varphi \chi \psi \omega A $$: $$\phi \chi \psi \omega A$$
$$ B \Gamma \varGamma \Delta \varDelta $$: $$B\Gamma \Gamma \Delta \Delta$$
$$ E Z H \Theta \varTheta $$: $$EZH\Theta \Theta$$
$$ I K \Lambda \varLambda M $$: $$IK\Lambda \Lambda M$$
$$ N \Xi \varXi O \Pi $$: $$N\Xi \Xi O\Pi$$
$$ \varPi P \Sigma \Upsilon \varUpsilon $$: $$\Pi P\Sigma {\rm Y}{\rm Y}$$
$$ \Phi \varPhi X \varPsi \Omega \varOmega$$: $$\Phi \Phi X\Psi \Omega \Omega$$

四. 一些公式

矩阵：
$$ \left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right]\tag{2}$$
[ 1 2 3 4 5 6 7 8 9 ] (2) \left[

$$\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}$$ \right]\tag{2} ⎣⎡​147​258​369​⎦⎤​(2)

分段函数：

$$
f(x) = \left\{
  \begin{array}{lr}
    x^2 & : x < 0\\
    x^3 & : x \ge 0
  \end{array}
\right.
$$

$$
u(x) = 
  \begin{cases} 
   \exp{x} & \text{if } x \geq 0 \\
   1       & \text{if } x < 0
  \end{cases}
$$
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

f ( x ) = { x 2 : x < 0 x 3 : x ≥ 0 f(x) = \left\{

$$\begin{array}{lr} x^2 & : x < 0\\ x^3 & : x \ge 0 \end{array}$$ \right. f(x)={x2x3​:x<0:x≥0​

u ( x ) = { exp ⁡ x if  x ≥ 0 1 if  x < 0 u(x) =

$$\begin{cases} \exp{x} & \text{if } x \geq 0 \\ 1 & \text{if } x < 0 \end{cases}$$ u(x)={expx1​if x≥0if x<0​
方程组：

$$
\left\{ 
\begin{array}{c}
    a_1x+b_1y+c_1z=d_1 \\ 
    a_2x+b_2y+c_2z=d_2 \\ 
    a_3x+b_3y+c_3z=d_3
\end{array}
\right. 
$$
1
2
3
4
5
6
7
8
9

{ a 1 x + b 1 y + c 1 z = d 1 a 2 x + b 2 y + c 2 z = d 2 a 3 x + b 3 y + c 3 z = d 3 \left\{

$$\begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array}$$ \right. ⎩⎨⎧​a1​x+b1​y+c1​z=d1​a2​x+b2​y+c2​z=d2​a3​x+b3​y+c3​z=d3​​

线性模型：

$$
h(\theta) = \sum_{j = 0} ^n \theta_j x_j
$$
1
2
3

$$h(\theta )=\sum _{j=0}^n{\theta }_j{x}_j$$

均方误差：

$$
J(\theta) = \frac{1}{2m}\sum_{i = 0} ^m(y^i - h_\theta (x^i))^2
$$
1
2
3

$$J(\theta )=\frac{1}{2m}\sum _{i=0}^m(y^i-h_{\theta }(x^i){)}^2$$

批量梯度下降：

$$
\frac{\partial J(\theta)}{\partial\theta_j}=-\frac1m\sum_{i=0}^m(y^i-h_\theta(x^i))x^i_j 
$$
1
2
3

$$\frac{\partial J(\theta )}{\partial {\theta }_j}=-\frac{1}{m}\sum _{i=0}^m(y^i-h_{\theta }(x^i))x_j^i$$

五. 关系符号和箭头符号

3.1 关系符号

$$
\bowtie    \Join    \propto    \varpropto    \multimap    \pitchfork  \therefore    \because    =    \neq    \equiv    \approx    \sim    \simeq    \backsimeq    \approxeq    \cong    \ncong        \smile    \frown    \asymp    \smallfrown    \smallsmile    \between    \prec    \succ    \nprec    \nsucc    \preceq    \succeq    \npreceq    \nsucceq    \preccurlyeq    \succcurlyeq    \curlyeqprec    \curlyeqsucc    \precsim    \succsim    \precnsim    \succnsim    \precapprox    \succapprox    \precnapprox    \succnapprox    \perp    \vdash    \dashv    \nvdash    \Vdash    \Vvdash    \models    \vDash    \nvDash    \nVDash    \mid    \nmid    \parallel    \nparallel    \shortmid    \nshortmid    \shortparallel    \nshortparallel    <    >    \nless    \ngtr    \lessdot    \gtrdot    \ll    \gg    \lll    \ggg    \leq    \geq    \lneq    \gneq    \nleq    \ngeq    \leqq    \geqq    \lneqq    \gneqq    \lvertneqq    \gvertneqq    \nleqq    \ngeqq    \leqslant    \geqslant    \nleqslant    \ngeqslant    \eqslantless    \eqslantgtr    \lessgtr    \gtrless    \lesseqgtr    \gtreqless    \lesseqqgtr    \gtreqqless    \lesssim    \gtrsim    \lnsim    \gnsim    \lessapprox    \gtrapprox    \lnapprox    \gnapprox    \vartriangleleft    \vartriangleright    \ntriangleleft    \ntriangleright    \trianglelefteq    \trianglerighteq    \ntrianglelefteq    \ntrianglerighteq    \blacktriangleleft    \blacktriangleright    \subset    \supset    \subseteq    \supseteq    \subsetneq    \supsetneq    \varsubsetneq    \varsupsetneq    \nsubseteq    \nsupseteq    \subseteqq    \supseteqq    \subsetneqq    \supsetneqq    \nsubseteqq    \nsupseteqq    \backepsilon    \Subset    \Supset    \sqsubset    \sqsupset    \sqsubseteq    \sqsupseteq
$$
1
2
3

$$\bowtie \bowtie \propto \propto ⊸⋔\therefore \because =\ne \equiv \approx \sim \simeq \backsimeq \approxeq \cong ≆⌣⌢\asymp ⌢⌣\between \prec \succ \nprec \nsucc ⪯⪰⋠⋡\preccurlyeq \succcurlyeq ⋞⋟\precsim \succsim ⋨⋩⪷⪸⪹⪺\perp ⊢⊣⊬⊩\Vvdash \models \models ⊭⊯\mid \nmid \parallel \nparallel \mid \parallel <>\nless \ngtr ⋖⋗\ll \gg ⋘⋙\le \ge ⪇⪈\nleqq \ngeqq \leqq \geqq \lneqq \gneqq ⩽⩾⪕⪖\lessgtr \gtrless ⋚⋛⪋⪌\lesssim \gtrsim ⋦⋧⪅⪆⪉⪊⊲⊳⋪⋫⊴⊵⋬⋭◀▶\subset \supset \subseteq \supseteq ⊊⊋⊈⊉⫅⫆⫋⫌∍⋐⋑⊏⊐⊑⊒$$

3.2 箭头符号

$$
\leftarrow    \leftrightarrow    \rightarrow    \mapsto    \longleftarrow        \longleftrightarrow    \longrightarrow    \longmapsto    \downarrow    \updownarrow    \uparrow    \nwarrow        \searrow    \nearrow    \swarrow        \nleftarrow            \nleftrightarrow        \nrightarrow        \hookleftarrow        \hookrightarrow        \twoheadleftarrow        \twoheadrightarrow        \leftarrowtail        \rightarrowtail        \Leftarrow        \Leftrightarrow        \Rightarrow        \Longleftarrow        \Longleftrightarrow        \Longrightarrow            \Updownarrow        \Uparrow        \Downarrow        \nLeftarrow        \nLeftrightarrow    \nRightarrow        \leftleftarrows        \leftrightarrows        \rightleftarrows        \rightrightarrows        \downdownarrows        \upuparrows        \circlearrowleft        \circlearrowright        \curvearrowleft        \curvearrowright        \Lsh        \Rsh        \looparrowleft        \looparrowright        \dashleftarrow        \dashrightarrow        \leftrightsquigarrow        \rightsquigarrow        \Lleftarrow        \leftharpoondown        \rightharpoondown        \leftharpoonup        \rightharpoonup        \rightleftharpoons        \leftrightharpoons        \downharpoonleft        \upharpoonleft        \downharpoonright            \upharpoonright
$$
1
2
3

$$\leftarrow \leftrightarrow \to \mapsto ⟵⟷⟶⟼\downarrow \updownarrow \uparrow \nwarrow \searrow \nearrow \swarrow \nleftarrow \nleftrightarrow \nrightarrow \hookleftarrow \hookrightarrow \twoheadleftarrow \twoheadrightarrow \leftarrowtail \rightarrowtail \Leftarrow \iff \Rightarrow ⟸⟺⟹\Updownarrow \Uparrow \Downarrow \nLeftarrow \nLeftrightarrow \nRightarrow \leftleftarrows \leftrightarrows \rightleftarrows \rightrightarrows \downdownarrows \upuparrows \circlearrowleft \circlearrowright \curvearrowleft \curvearrowright \Lsh \Rsh \looparrowleft \looparrowright ⇠⇢\leftrightsquigarrow ⇝\Lleftarrow \leftharpoondown \rightharpoondown \leftharpoonup \rightharpoonup \rightleftharpoons \leftrightharpoons \downharpoonleft \upharpoonleft \downharpoonright \upharpoonright$$

六. 其它

行间公式：$$\frac{d}{dx}e^{ax}=ae^{ax}\quad \sum_{i=1}^{n}{(X_i - \overline{X})^2}$$: $$\frac{d}{dx}{e}^{ax}=a{e}^{ax}\sum _{i=1}^n(X_i-\overline{X}{)}^2$$

省略号：

• $$\cdots 和 \ldots$$: $$\cdots 和\dots$$
• $$ {1+2+3+\ldots+n} $$: $$1+2+3+\dots +n$$

行内公式: $R^s_r(t_r,t_e)=(t_r-t_e)c$: $R_r^s(t_r,t_e)=(t_r-t_e)c$

显示公式: $$R^s_r(t_r,t_e)=(t_r-t_e)c$$: $$R_r^s(t_r,t_e)=(t_r-t_e)c$$

$$\frac{\partial f(x,y)}{\partial x}$$: $$\frac{\partial f(x,y)}{\partial x}$$