| A | B |
|---|
| Closure axiom of addition | a+b= a real number |
| Closure axiom of multiplication | a*b= a real number |
| Commutative axiom for addition | a+b= b+a |
| Commutative axiom for multiplication | a*b=b*a |
| Identity axiom for addition | a+0=a |
| Identity axiom for multiplication | a*(1)=a |
| Inverse for addition | a+(-a)=0 |
| Inverse for multiplication | a*(1/a)=1 |
| Associative axiom for addition | (a+b)+c=a+(b+c) |
| Associative axiom for multiplication | (ab)c=a(bc) |
| Distributive axiom | a(b+c)=ab+ac |
