A proof is a logical and structured argument to show that a mathematical statement (or conjecture) is always true.

Proof by deduction starts from known facts or definitions (or theorems), then uses logical steps to reach the desired conclusion.

Statements which are assumed to be true include:

• All even numbers can be written as 2n.
• All odd numbers can be written as 2n+1.

Proof by deduction involves:

1. Start with a statement, and assume that it is true.
2. Use this statement to show that another statement must be true.
3. Finish with a statement of proof.