Part 3/6:
The critical point in this fallacious proof lies in the division by zero. The assertion that ( \frac{a - b}{a - b} = 1 ) is only valid when ( a \neq b ); otherwise, it becomes ( \frac{0}{0} ), which is undefined. This fundamental error unveils the potential for mathematical expressions to lead to nonsensical results.
By demonstrating the ambiguous outcome that arises when equating zero, the discussion reveals that if one were to incorrectly assume that division by zero holds merit, one could reach absurdities such as asserting that ( 1 = 2 ) or any two distinct numbers being equal.