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数式の練習

Last updated at Posted at 2016-12-20

Qiitaの数式チートシート を参考にした。

関数

\begin{align}
f: \, &X \rightarrow Y \\
&x \mapsto f(x)
\end{align}

行列

\begin{pmatrix}
a & b \\
c & d 
\end{pmatrix}
\\
\begin{bmatrix}
a & b \\
c & d 
\end{bmatrix}
\\
\begin{vmatrix}
a & b \\
c & d 
\end{vmatrix}

分数

\frac{1}{2} - \frac{1}{3} = \frac{1}{6} \\
1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{2}}}}}

e

e = 2.71828...

黄金比

\phi = \frac{1 + \sqrt{5}}{2} = 1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \cdots}}}

関数合成

\begin{align}
&f^{[1]} = f \\
&f^{[2]} = f \circ f \\
&f^{[n]} = \overbrace{f \circ f \circ \cdots \circ f}^{ n }
\end{align}
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