The set of integers, Z, is
Closed: if x and y are in Z then so is x ~ y, where ~ stands for either addition or multiplication.
Commutative: For all x, y in Z, x ~ y = y ~ x
Transitive: For all w, x, y in Z, (w ~ x) ~ y = w ~ (x ~ y)
Identity: Z contains a unique identity element, i, with the property that x ~ i = x for all x in Z. The additive identity is 0, the multiplicative identity is 1.
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The set of integers is closed with respect to multiplication and with respect to addition.
Closure with respect to addition and multiplication. Cummutative, Associative properties of addition and of multiplication. Distributive property of multiplication over addition.
Addition is not distrbutive over multiplication. In general,a + (b*c) ≠(a+b)*(a+c) [unless a+b+c = 1]
No because the commutative property only works for addition and multiplication
It means nothing, really. The distributive property is a property of multiplication over addition or subtraction. It has little, if anything, to do with integers.