比较两个实数的大小
作差法
a>b<span class="equation-text" data-index="0" data-equation="\Leftrightarrow" contenteditable="false"><span></span><span></span></span>a-b>0;a=b<span class="equation-text" data-index="1" data-equation="\Leftrightarrow" contenteditable="false"><span></span><span></span></span>a-b=0;a<b<span class="equation-text" contenteditable="false" data-index="2" data-equation="\Leftrightarrow"><span></span><span></span></span>a-b<0
作商法
<span class="equation-text" data-index="0" data-equation="\frac{a}{b}" contenteditable="false"><span></span><span></span></span>>1<span class="equation-text" data-index="1" data-equation="\Leftrightarrow" contenteditable="false"><span></span><span></span></span>a>b;<span class="equation-text" data-index="2" data-equation="\frac{a}{b}" contenteditable="false"><span></span><span></span></span>=1<span class="equation-text" data-index="3" data-equation="\Leftrightarrow" contenteditable="false"><span></span><span></span></span>a=b;<span class="equation-text" contenteditable="false" data-index="4" data-equation="\frac{a}{b}"><span></span><span></span></span><1<span class="equation-text" data-index="5" data-equation="\Leftrightarrow" contenteditable="false"><span></span><span></span></span>a<b
等式的性质
对称性：a=b<span class="equation-text" contenteditable="false" data-index="0" data-equation="\Leftrightarrow"><span></span><span></span></span>b=a
传递性：a=b,b=c<span class="equation-text" contenteditable="false" data-index="0" data-equation="\Rightarrow"><span></span><span></span></span>a=c
可加性：a=b<span class="equation-text" data-index="0" data-equation="\Leftrightarrow" contenteditable="false"><span></span><span></span></span>a<span class="equation-text" data-index="1" data-equation="\pm" contenteditable="false"><span></span><span></span></span>c=b<span class="equation-text" contenteditable="false" data-index="2" data-equation="\pm"><span></span><span></span></span>c
可乘性：a=b<span class="equation-text" contenteditable="false" data-index="0" data-equation="\Rightarrow"><span></span><span></span></span>ac=bc
可除性：a=b,c≠0⇒<span class="equation-text" data-index="0" data-equation="\frac{a}{c}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" contenteditable="false" data-index="1" data-equation="\frac{b}{c}"><span></span><span></span></span>
不等式的性质
对称性：a>b<span class="equation-text" contenteditable="false" data-index="0" data-equation="\Leftrightarrow"><span></span><span></span></span>b<a
传递性：a>b,b>c<span class="equation-text" contenteditable="false" data-index="0" data-equation="\Rightarrow"><span></span><span></span></span>a>c
可加性：a>b<span class="equation-text" contenteditable="false" data-index="0" data-equation="\Rightarrow"><span></span><span></span></span>a+c>b+c
可乘性：a>b,c>0<span class="equation-text" data-index="0" data-equation="\Rightarrow" contenteditable="false"><span></span><span></span></span>ac>bc;a>b,c<0<span class="equation-text" contenteditable="false" data-index="1" data-equation="\Rightarrow"><span></span><span></span></span>ac<bc
同向可加性：a>b,c>d<span class="equation-text" contenteditable="false" data-index="0" data-equation="\Rightarrow"><span></span><span></span></span>a+c>b+d
同向可乘性：a>b>0,c>d>0<span class="equation-text" contenteditable="false" data-index="0" data-equation="\Rightarrow"><span></span><span></span></span>ac>bd
可乘方性：a>b>0<span class="equation-text" data-index="0" data-equation="\Rightarrow" contenteditable="false"><span></span><span></span></span><span class="equation-text" data-index="1" data-equation="a^n" contenteditable="false"><span></span><span></span></span>><span class="equation-text" contenteditable="false" data-index="2" data-equation="b^n"><span></span><span></span></span>(nN,n>1)
