What are the rules of integers?

Updated: 4/28/2022
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6y ago

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To start with, the set of integers is a Group. This means that it is a set of elements (numbers) with a binary operation (addition) that combines any two elements in the set to form a third element. This Group, Z, satisfies four axioms: closure, associativity, identity and invertibility. that is, if x , y and z are integers, then

  • x + y is an integer (closure).
  • (x + y) + z = x + (y + z) (associativity)
  • there is an integer, denoted by 0, such that 0 + x = x + 0 = x
  • there is an integer, denoted by -x, such that x + (-x) = (-x) + x = 0.

In addition, it is a Ring. A ring is an Abelian group (that is, addition is commutative: x + y = y + x) and it has a second binary operation (multiplication) that is defined on its elements. This second operation satisfies the axioms of closure, associativity and identity. It is also distributive over the first operation. That is,

  • x*(y + z) = x*y + x*z

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Integers are whole numbers without decimals or fractions

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Q: What are the rules of integers?
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The rules are the same.

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