# 不等

（重定向自不相等

• ${\displaystyle a，即${\displaystyle a}$小于${\displaystyle b}$
• ${\displaystyle a>b}$，即${\displaystyle a}$大于${\displaystyle b}$

• ${\displaystyle a\leq b}$，即${\displaystyle a}$小于等于${\displaystyle b}$
• ${\displaystyle a\geq b}$，即${\displaystyle a}$大于等于${\displaystyle b}$
• ${\displaystyle a\neq b}$，即${\displaystyle a}$不等于${\displaystyle b}$

## 性质

• ${\displaystyle a
• ${\displaystyle a=b}$
• ${\displaystyle a>b}$

• ${\displaystyle a>b}$ ；则 ${\displaystyle a+c>b+c}$
• ${\displaystyle a ；则 ${\displaystyle a+c

• ${\displaystyle c}$ 正数${\displaystyle a>b}$ ；则 ${\displaystyle ac>bc}$
• ${\displaystyle c}$ 为 正数 且 ${\displaystyle a ；则 ${\displaystyle ac
• ${\displaystyle c}$ 负数${\displaystyle a>b}$ ；则 ${\displaystyle ac
• ${\displaystyle c}$ 为 负数 且 ${\displaystyle a ；则 ${\displaystyle ac>bc}$

## 举例

• ${\displaystyle x>0}$  ；则
${\displaystyle x^{x}\geq \left({\frac {1}{e}}\right)^{\frac {1}{e}},}$
• ${\displaystyle x>0}$ ；则
${\displaystyle x^{x^{x}}\geq x\,}$
• ${\displaystyle x,y,z>0}$ ；则
${\displaystyle (x+y)^{z}+(x+z)^{y}+(y+z)^{x}>2\,}$
• ${\displaystyle x,y,z>0}$ ；则
${\displaystyle x^{x}y^{y}z^{z}\geq (xyz)^{\frac {x+y+z}{3}},}$
• ${\displaystyle a,b>0}$ ；则
${\displaystyle a^{a}+b^{b}\geq a^{b}+b^{a}\,}$
• ${\displaystyle a,b>0}$ ；则
${\displaystyle a^{ea}+b^{eb}\geq a^{eb}+b^{ea}\,}$
• ${\displaystyle a,b,c>0}$ ；则
${\displaystyle a^{2a}+b^{2b}+c^{2c}\geq a^{2b}+b^{2c}+c^{2a}\,}$
• ${\displaystyle a_{1},\ldots ,a_{n}>0}$ ；则
${\displaystyle a_{1}^{a_{2}}+a_{2}^{a_{3}}+\cdots +a_{n}^{a_{1}}>1}$