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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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Is the product of two integers positive negative or zero How can you tell?
The product of two integers will be: * Zero, if one factor, or both, are zero. * Positive, if both factors have the same sign (both positive, or both negative) * Negative, if the two factors have different signs. Actually, these rules apply to all real numbers, not just to integers.
When the negative integers the positive integers and 0 are combined the integers are formed?
Negative integers, zero and the positive integers, together form the set of integers.
Which set is the intersection of integers and rational numbers?
The intersection of integers and rational numbers is the set of integers. Integers are whole numbers that can be positive, negative, or zero, while rational numbers are numbers that can be expressed as a ratio of two integers. Since all integers can be expressed as a ratio of the integer itself and 1, they are a subset of rational numbers, making their intersection the set of integers.
What are two consecutive integers is 200 between?
"Consecutive" integers are integers that have no other integer between them.
How many integers between 1 and 1000 are the products of two consecutive integers?
There are 30 such integers.
