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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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Q: What is a property of integers pertaining to both addition and multiplication?
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