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What does this mean Which set of these numbers is closed under subtraction?
It means whatever members of the set you subtract, the answer will still be a member of the set. For example, the set of positive integers is not closed under subtraction, since 3 - 8 = -5
Is the set of integers that are multiple of 4 is closed under subtraction?
Yes.
What operation is the set of positive rational numbers not closed?
subtraction. Let's take 1/2 and subtract 3/4 which is great than 1/2 so the answer is negative and hence not a positive rational.
What do interger's allow you to do that whole numbers do not?
Integers are closed under subtraction, meaning that any subtraction problem with integers has a solution in the set of integers.
Can the operation subtraction have properties?
Not by itself. A mathematical operation has properties in the context of a set over which it is defined. It is possible to have a set over which properties are not valid.Having said that, the set of rational numbers is closed under subtraction, as is the set of real numbers or complex numbers.Multiplication is distributive over subtraction.
