Working with variables and solving equations are often considered the basis of algebra. An equation is a mathematical sentence, a relationship between numbers and/or symbols.
For all real numbers a, b, and c, the following are some basic rules (axioms) for using the equal sign.
Reflexive axiom: a = a.
Therefore, 4 = 4.
Symmetic axiom: If a = b, then b = a.
Therefore, if 2 + 3 = 5, then 5 = 2 + 3.
Transitive axiom: If a = b and b = c, then a = c.
Therefore, if 1 + 3 = 4 and 4 = 2 + 2, then 1 + 3 = 2 +2.
Additive axiom: If a = b and c = d, then a + c = b + d.
Therefore, if 1 + 1 = 2 and 3 + 3 = 6, then 1 + 1 + 3 + 3 = 2 + 6.
Multiplicative axiom: If a = b and c = d, then ac = bd.
Therefore, if 1 = 2/2 and 4 = 8/2, then 1(4) = (2/2)(8/2).
