Any one of the sets of the form:
{kz : where k is any fixed integer and z belongs to the set of all integers}
Thus, k = 1 gives the set of all integers,
k = 2 is the set of all even integers,
k = 3 is the set of all multiples of 3,
and so on.
You might think that as k gets larger the sets become smaller because the gaps between numbers in the set increases. However, it is easy to prove that the cardinality of each of these infinite sets is the same.
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A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
It depends on your definition of whole numbers. The classic definition of whole numbers is the set of counting numbers and zero. In this case, the set of whole numbers is not closed under subtraction, because 3-6 = -3, and -3 is not a member of this set. However, if you use whole numbers as the set of all integers, then whole numbers would be closed under subtraction.
The set of rational numbers is closed under all 4 basic operations.
Please clarify what set you are talking about. There are several sets of numbers. Also, "closed under..." should be followed by an operation; "natural" is not an operation.