Let's begin by looking at a few definitions that will help give a clearer understanding of what this section is about.  

An axiom or postulate is a statement that is assumed to be true but is not supported by proof.

A theorem is a statement that has been proven true through the use of axioms, definitions, and other theorems. 

A proof uses axioms in a logical order to show that a statement is true. 

Natural numbers are the numbers we
use to count.  For example: 1, 2, 3, 4...

Remember, when we count a group of objects, the first number we start with is 1, not zero. 

Integers are positive and negative numbers on a number line. 
For example:
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Math:  Axioms, Properties, and Rules
Below are some axioms, definitions, and rules for proving statements.  Let's get started!