Term | Definition |
Closure prop. of Addition | For any a and b in R, the sum a+b is in R. |
Closure prop. of Multiplication | For any a and b in R, the product a・b is in R. |
Associative prop. of Addition | For any a, b, and c in R, (a + b) + c = a + (b + c). |
Associative prop. Multiplication | For any a, b, and c in R, (a ・ b) ・ c = a ・ (b ・ c). |
Commutative prop. of Addition | For any a and b in R, a + b = b + a. |
Commutative prop. of Multiplication | For any a and b in R, a ・ b = b ・ a. |
Distributive prop. of Multiplication over Addition | For any a, b, and c in R, (a + b) ・ c = (a ・ c) + (b ・ c). |
Multiplicative Identity | There is a unique number 1 in R such that for any a in R, a ・ 1 = a. |
Reflexive prop. of Equality | For any a in R, a = a. |
Symmetric prop. of Equality | For any a and b in R, if a = b, then b = a. |
Transitive prop. of Equality | For any a, b, and c in R, if a = b and b = c, then a = c. |
Addition prop. of Equality | For any a, b, and c in R. if a = b, then a + c = b + c. |
Multiplication prop. of Equality | For any a, b, and c in R. if a = b, then a ・ c = b ・ c. |