Checking a Deductive Argument

A proof starts from facts already known and uses justified steps to reach its conclusion. A numerical check can detect an error, but agreement in several cases does not establish an identity. Before calculating, state the domain. Record every value excluded by a denominator or logarithm; these restrictions remain after simplification. When proving an identity, choose one side and transform it into the other. Writing the required equality first and rearranging it until a true statement appears does not explain why the starting equality was valid unless every step is reversible and that reasoning is explicitly stated. For example, squaring both sides of an equation can introduce extra solutions: x=-2 does not follow from x2=4. Division by a variable can lose its zero case. Check candidate solutions in the original statement. In a direct integer argument, finish by naming the property established: 2k is even because k is an integer. A formula without this domain statement leaves the reason incomplete. For an exact numerical equality, keep fractions and radicals exact. A rounded decimal agreement is only an approximation check. After the proof, a simple admissible substitution is a useful independent arithmetic check.