The explanation given in the paint document that I copied from a book does not seem complete. They are saying that the sum of two numbers is least when the two numbers are equal. Here is my explanation for why this is not always true. Let a and b be two positive numbers. I will denote the sum S1 as 2a and the sum S2 as a + b Then I can say that S1>S2 if a>b and therefore S1 = S2 for b = a which is greater than S2 for a>b. Second explanation: Let a and b be a positive number and I will define the sum S1 to be the sum of a finite number of n terms therefore S1 = na = M = M + (b-b) = M + 0 If I allow M = na to equal the second term in S1 then I have na = 0 or a = 0, however I defined n to be positive and therefore a must equal itself. and therefore I can conclude that na>0 or S1> n*0 = 0 where RHS is equal to the sum of n zeros. Am I misinterpreting what they are saying in the paint document?