實數分類
- 實數按定義分類：
\[實數\R\left\{\begin{array}{l}{有理數\Q\left\{\begin{array}{l}{整數\Z\left\{\begin{array}{l}{正整數\N_+}\\{零}\\{負整數\N_-}\end{array}\right\}正整數\&零\Rightarrow 自然數\N}\\{分數\left\{\begin{array}{l}{正分數}\\{負分數}\end{array}\right\}有限小數或無限循環小數\Rightarrow 小數}\end{array}\right.}\\{無理數C_{\R}{\Q}\Leftrightarrow 無限不循環小數\Rightarrow 小數}\end{array}\right. \]
- 實數按大小分類：
\[實數\left\{\begin{array}{l}{正實數\left\{\begin{array}{l}{正有理數\left\{\begin{array}{l}{正整數}\\{正分數}\end{array}\right.}\\{正無理數}\end{array}\right.}\\{零}\\{負實數\left\{\begin{array}{l}{負有理數\left\{\begin{array}{l}{負整數}\\{負分數}\end{array}\right.}\\{負無理數}\end{array}\right.}\end{array}\right. \]
復數分類
\(復數\C：z=a+bi(a,b\in R)\left\{\begin{array}{l}{實數\R:b=0}\\{虛數:b\neq 0\left\{\begin{array}{l}{純虛數:a=0}\\{混虛數:a\neq 0}\end{array}\right.}\end{array}\right.\)