A good proof has the following properties:
Justify each step
Write your proofs in two-column format, with each step showing a true statement in the left column and a correct justification on the right.
Statements have truth value; expressions do not. For example, an equation is either true or not. Thus, no step should consist of just an algebraic expression.
Each step must also be justified. If you cannot provide a clear and convincing reason for a particular statement in your proof, then you need to give the matter further thought and consider adding additional steps to improve the argument.
The last step is the conclusion, namely the statement which you set out to prove.
See the proofs on the example proofs page.
A bad proof may have the following properties:
The first step is a restatement of the result to be proven.
Any step is a simple expression with some value other than true or false.
Any step violates type constraints; e.g., a step that equates a number to a set cannot be valid. Use your mental type-checker!
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