ABSTRACT
This chapter focuses on a more meaty topic: how to prove that a given statement is true, turning it into a theorem. Some of the basic statements posit the existence of an object. To prove that such a statement is true, one simply must show that such an object exists. There are a few ways to accomplish this, but the most basic one is given: To prove a statement that posits the existence of an object, one strategy is to simply give an example of such an object. Many of the most basic universal statements posit that all objects of a certain type will have a certain property. To prove such a statement is true, one must show that every qualifying object has this certain property. A proof by induction is a proof for a very special kind of mathematical statement, that says (in a certain sense) that infinitely many similar statements are all simultaneously true.
