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for a>b>0
|a+b|=a+b
|a|+|b|=a+b
so |a+b|=|a|+|b|
for a>0>b,a>|b|
|a+b|=a+b
|a|+|b|=a+|b|
so |a+b|<|a|+|b| (|b|>b)
for a>0>b,a<|b|
|a+b|=|b|-a
|a|+|b|=a+|b|
so |a+b|<|a|+|b| (a>-a)
for 0>a>b
|a+b|=-(a+b)
|a|+|b|=(-a)+(-b)=-(a+b)
so |a+b|=|a|+|b|
for a=0
|a+b|=|0+b|=|b|
|a|+|b|=|0|+|b|=|b|
so |a+b|=|a|+|b|
for a=b
|a+b|=|a+a|=|2a|=2|a|
|a|+|b|=|a|+|a|=2|a|
so |a+b|=|a|+|b|
combine all case,
|a+b|≦|a|+|b|
其他case都一樣做法
其實prove黎無謂
學上面話齋
呢d野都好logic |
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