The proof is in the document. I highlighted the main points that I am questioning in the document. I am questioning the fact that A = B... (The following is in the document) |A-B|=ε where they define the value of ε to be a positive arbitrary real number (ε>0). And for A = B that means ε must be equal to zero however ε>0. My Reasoning For A≥B we have A - B = ε And for B≥A we have A - B = -ε And after solving the system of two eq. A - B = ε & A - B = -ε we get A - B = 0 ∴ A = B. Is this how they proved A is the same as B?