Hello all, I’m evidently not an expert on Mathematics but I still want to question the consistency of this system. How confident can we really be that there aren’t any big flaws? I have done some research and have found the following paradoxes which I can’t explain. Assume that a = b Multiplying both sides by a, a² = ab Subtracting b² from both sides, a² - b² = ab - b² Factorizing both sides, (a + b)(a - b) = b(a - b) Dividing both sides by (a - b), a + b = b Sinse a = b, we substitute and get b + b = b So, 2b = b Devide by b 2 = 1 There is another one... Assume A + B = C, and assume A = 3 and B = 2. Multiply both sides of the equation A + B = C by (A + B). We obtain A² + 2AB + B² = C(A + B) Rearranging the terms we have A² + AB - AC = - AB - B² + BC Factoring out (A + B - C), we have A(A + B - C) = - B(A + B - C) Dividing both sides by (A + B - C), that is, dividing by zero, we get A = - B, or A + B = 0, which is evidently absurd.