Verification: for any real number a and B, there is │ a + B │ ≤ │ a + │ B │. (hint: for any real number a, there is - │ a │ ≤ a ≤ │ a │)

Verification: for any real number a and B, there is │ a + B │ ≤ │ a + │ B │. (hint: for any real number a, there is - │ a │ ≤ a ≤ │ a │)

∵ for any real number a, B
-│a│≤a≤│a│
-|b|≤b≤|b|
The sum of the two formulas:
-(|a|+|b|)≤a+b≤|a|+|b|
∴│a+b│≤│a│+│b│