集合

$\left\{ \begin{gathered} {\text{N} } \to 0,1,2 \cdots \hfill \\ { {\text{N} }^*}{\text{/} }{ {\text{N} }_ + } \to 1,2 \cdots \hfill \\ \Z \to - 2, - 1,0,1,2 \cdots \hfill \\ \Q \to - 1.3,\frac{5}{3},6 \cdots \hfill \\ \R \to \sqrt 3 ,\pi ,3 \cdots \hfill \\ \end{gathered} \right.$ $\emptyset \subseteq A,A \subseteq A$ $\left\{ \begin{gathered} A \cap B = \left\{ {x|x \in A,且x \in B} \right\}\\ A \cup B = \left\{ {x|x \in A,或x \in B} \right\} \end{gathered} \right.$ ${\complement _U}A = \left\{ {x|x \in U,且x \notin A} \right\}$ $\left\{ \begin{gathered} {\complement _U}(A \cap B) = ({\complement _U}A) \cup ({\complement _U}B) \hfill \\ {\complement _U}(A \cup B) = ({\complement _U}A) \cap ({\complement _U}B) \hfill \\ \end{gathered} \right.$ $p\Rightarrow q\Longleftrightarrow p是q的充分条件\\ p\Leftarrow q\Longleftrightarrow p是q的必要条件\\ \left\{ \begin{gathered} p \Rightarrow q \hfill \\ p \Leftarrow q \hfill \\ \end{gathered} \right.\Longleftrightarrow p 是q的充要条件$ $\tan x:\left\{ {x \in \mathbb{R},x \ne \frac{\pi }{2} + k\pi ,k \in \mathbb{Z}} \right\}\\ \frac{1}{x}: x \ne 0 \quad\sqrt[{2k}]{x} :\left\{ {x \in \mathbb{R},x \geqslant 0} \right\}\\ {\log _a}x:a > 0,a \ne 1,x > 0\;x^0:x\ne0\\ \cot x:\left\{ {x \in \mathbb{R},x \ne k\pi ,k \in \mathbb{Z}} \right\} \\$ $\left\{ {\begin{array}{*{20}{l}} {\frac{1}{6} = 0.1666 \ldots } \\ {\frac{5}{6} = 0.8333 \ldots } \end{array}} \right.\\\left\{\begin{array}{l} \frac{2}{6}=0.3333 \ldots \\ \frac{4}{6}=0.6666 \ldots \end{array}\right.$ $\left\{\begin{array}{c} \frac{1}{9}=0.1111 \ldots \\ \frac{2}{9}=0.2222 \ldots \\ \frac{3}{9}=0 . \dot{3} \\ \ldots \end{array}\right.$ $\left\{\begin{aligned} \frac{1}{7} &=0.142857,142857,14 \ldots \\ \frac{2}{7} &=0.2857,142857,1428 \ldots \\ \frac{4}{7} &=0.57,142857,142857 \ldots \end{aligned}\right.$ $\left\{\begin{array}{c} \frac{1}{11}=0.090909 \ldots \\ \frac{2}{11}=\overline{0 . \dot{1} \dot{8}} \\ \frac{3}{11}=\overline{0 . \dot{2} \dot{7}} \\ \ldots \end{array}\right.$