An *Axiom* is a mathematical statement that is assumed to be true.
There are five basic axioms of algebra. The axioms are
the reflexive axiom, symmetric axiom, transitive axiom, additive axiom and multiplicative axiom.

*Reflexive Axiom:* A number is equal to itelf. (e.g a = a). This is the first axiom of equality.
It follows Euclid's Common Notion One: "Things equal to the same thing are equal to each other."

*Symmetric Axiom:* Numbers are symmetric around the equals sign. If a = b then b = a. This is the second axiom of equality
It follows Euclid's Common Notion One: "Things equal to the same thing are equal to each other."

*Transitive Axiom:* If a = b and b = c then a = c. This is the third axiom of equality.
It follows Euclid's Common Notion One: "Things equal to the same thing are equal to each other."

*Additive Axiom:* If a = b and c = d then a + c = b + d. If two quantities are equal and an equal
amount is added to each, they are still equal.

*Multiplicative Axiom:* If a=b and c = d then ac = bd. Since multiplication is just repeated addition,
the multiplicative axiom follows from the additive axiom.