Dowód wartości bezwzględnej Tao Cat Agent : Udowodnij twierdzenie ⋀ a,b∊ℛ(|x+y|≤|x|+|y|) 1) x>0 i y>0 |x+y|=x+y |x|+|y|=x+y |x+y|=|x|+|y| 2) x<0 i y<0 |x+y|=−x−y |x|+|y|=−x−y |x+y|=|x|+|y| 3) x>0 i y<0 i x+y>0 |x+y|=x+y i |x|+|y|=x−y i ale y<0 to x+y<x−y to |x+y|<|x|+|y| 4) x>0 i y<0 i x+y<0 |x+y|=−x−y i |x|+|y|=x−y ale x>0 to −x−y<x−y to |x+y|<|x|+|y| 5) x=0 x=0 to |x+y|=|y| i |x|+|y|=|y| to |x+y|=|x|+|y| 6) y=0 to |x+y|=|x| i |x|+|y|=|x| to |x+y|=|x|+|y|