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Sagot :
Properties of addition and multiplication on integers
Addition Multiplication Closure: a + b is an integer a × b is an integer Associativity: a + (b + c) = (a + b) + c a × (b × c) = (a × b) × c Commutativity: a + b = b + a a × b = b × a Existence of an identity element: a + 0 = a a × 1 = a Existence of inverse elements: a + (−a) = 0 An inverse element usually does not exist at all. Distributivity: a × (b + c) = (a × b) + (a × c) and (a + b) × c = (a × c) + (b × c) No zero divisors: (*)
If a × b = 0, then a = 0 or b = 0 (or both)
Addition Multiplication Closure: a + b is an integer a × b is an integer Associativity: a + (b + c) = (a + b) + c a × (b × c) = (a × b) × c Commutativity: a + b = b + a a × b = b × a Existence of an identity element: a + 0 = a a × 1 = a Existence of inverse elements: a + (−a) = 0 An inverse element usually does not exist at all. Distributivity: a × (b + c) = (a × b) + (a × c) and (a + b) × c = (a × c) + (b × c) No zero divisors: (*)
If a × b = 0, then a = 0 or b = 0 (or both)
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