Properties of Real Numbers

All real numbers have the following properties:

(1) Reflexive Property

For any real number a, a = a.
Example: 3 = 3, y = y, x + z = x + z (x, y and z are real numbers)

(2) Symmetric Property

For any real numbers a and b, if a = b, then b = a.
Example: If 3 = 1 + 2, then 1 + 2 = 3

(3) Transitive Property

For any real numbers a, b and c, if a = b and b = c, then a = c.
Example: If 2 + 3 = 5 and 5 = 1 + 4, then 2 + 3 = 1 + 4.

(4) Substitution Property

For any real numbers a and b, if a = b, then a may be replaced by b, and b may be replaced by a, in any mathematical statement without changing the meaning of the statement.

Example: If a = 3 and a + b = 5, then 3 + b = 5.

(5) Trichotomy Property

For any real numbers a and b, one and only one of the following conditions holds:

(1) a is greater than b ( a > b)
(2) a is equal to b ( a = b)
(3) a is less than b ( a < b)

Example: 3 < 4 , 4 + 2 = 6 , 7 > 5