ABSTRACT
The history of mathematics is replete with examples where observation and intuition led mathematicians to correct conclusions. This chapter reviews some of the different proof techniques that every mathematics student should be familiar with and that relate in one form or another to the secondary school curriculum, not to mention all of mathematics. The first type of proof one speak about is one that people have used throughout school and is called direct proof. The first example of a direct proof concerns a result that is used quite often in mathematics. In a proof by contradiction, sometimes known as an indirect proof, readers are trying to prove that a statement is true. A conjecture is a statement of a relationship that one believes is true based on evidence or intuition, or both, but is not yet proven. The idea behind mathematical induction is very intuitive and is illustrated by the dominoes launch.
