The basic algebraic properties of real numbers a,b and c are:
1. Closure: a + b and ab are real numbers
2. Commutative: a + b = b + a, ab = ba
3. Associative: (a+b) + c = a + (b+c), (ab)c = a(bc)
4. Distributive: (a+b)c = ac+bc
5. Identity: a+0 = 0+a = a
6. Inverse: a + (-a) = 0, a(1/a) = 1
7. Cancelation: If a+x=a+y, then x=y
8. Zero-factor: a0 = 0a = 0
9. Negation: -(-a) = a, (-a)b= a(-b) = -(ab), (-a)(-b) = ab