in reference to the formula you posted on my talk page as being proof of addition by subtraction fine in theory as i have yet to see of anything but i can prove that nothing is gained in your equation observe a b multiply both sides by a and you get a ab add a to both sides to get a a a ab using addition we get a a ab subtract ab from both sides a ab a ab ab thus a ab a ab combining terms on the lhs a ab a ab divide both sides by a ab a ab a ab a ab a ab cancel out like terms and viola we now see so nothing is gained from addition by subtraction fin