Summary
“Solution”: Let $ a=b \neq 0$. Then $ a^2 = ab$, and $ a^2 – b^2 = ab – b^2$. Factoring gives us $ (a+b)(a-b) = b(a-b)$. Canceling both sides, we have $ a+b = b$, but remember that $ a = b$, so $ 2b = b$. Since $ b$ is nonzero, we may divide both sides to obtain $ 2=1$, as desired. Explanation: This statement, had we actually proved it, would imply that all numbers are equal, since subtracting 1 from both sides gives $ 0=1$ and hence $ a=0$ for all real numbers $ a$....