实数分类
- 实数按定义分类：
\[实数\R\left\{\begin{array}{l}{有理数\Q\left\{\begin{array}{l}{整数\Z\left\{\begin{array}{l}{正整数\N_+}\\{零}\\{负整数\N_-}\end{array}\right\}正整数\&零\Rightarrow 自然数\N}\\{分数\left\{\begin{array}{l}{正分数}\\{负分数}\end{array}\right\}有限小数或无限循环小数\Rightarrow 小数}\end{array}\right.}\\{无理数C_{\R}{\Q}\Leftrightarrow 无限不循环小数\Rightarrow 小数}\end{array}\right. \]
- 实数按大小分类：
\[实数\left\{\begin{array}{l}{正实数\left\{\begin{array}{l}{正有理数\left\{\begin{array}{l}{正整数}\\{正分数}\end{array}\right.}\\{正无理数}\end{array}\right.}\\{零}\\{负实数\left\{\begin{array}{l}{负有理数\left\{\begin{array}{l}{负整数}\\{负分数}\end{array}\right.}\\{负无理数}\end{array}\right.}\end{array}\right. \]
复数分类
\(复数\C：z=a+bi(a,b\in R)\left\{\begin{array}{l}{实数\R:b=0}\\{虚数:b\neq 0\left\{\begin{array}{l}{纯虚数:a=0}\\{混虚数:a\neq 0}\end{array}\right.}\end{array}\right.\)