what are the 2 equality axioms of real numbers and the 5 axioms of order? And can you give examples? Thank You!

The 2 equality axioms of real numbers are as
follows:

1) Reflexive axiom of
equality which states that a = a, or any real number equals itself.  
Example:  5=5

2) Symmetric axiom of
equality which states that if a = b, then b = a. Example:  12/4 = 3, then
3 = 12/4

There are 4 aximoms of order for
real numbers are as
follows:

1) Axiom of
comparison which states that for real numbers only one of the following
relationships can exist:  a > b; a < b; or a = b. Some examples are as
follows:

If a = 5 and b = 4, then 5 >
4

If a = 4 and b =5, a<
b

If a = 5 and b = 5, then a =
b.

2) Transitive axiom of
comparison which states if a < b and b < c, then a <
c.

Example:  if a = 4; b =5 and c = 6,  then the following
is true:  4 < 5 and 5< 6, therefore 4 <
6.

3) Multiplication axiom of
comparison which states the following:

If a
< b and c > 0, then ac < bc

Example: 
if a = 4, b = 5, and c =6, then (4)(5) <
(5)(6)

4) Additive axiom of
comparison which states the following:

If a
< b then a + c < b +c

Example:  if a = 4, b =
5, and c = 6, then 4 + 6 < 5 + 6