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Q: Why are the set of real numbers is not commuted under subtraction and addition?

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Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.

Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.

The set of rational numbers is closed under all 4 basic operations.

They form a closed set under addition, subtraction or multiplication.

Yes. The entire set of natural numbers is closed under addition (but not subtraction). So are the even numbers (but not the odd numbers), the multiples of 3, of 4, etc.

Yes. In general, the set of rational numbers is closed under addition, subtraction, and multiplication; and the set of rational numbers without zero is closed under division.

There is no counterexample because the set of whole numbers is closed under addition (and subtraction).

Yes they are closed under multiplication, addition, and subtraction.

If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.

Because subtraction is addition and division is multiplication. So, subtraction would fall under the properties of addition and division would come under the properties of multiplication.

No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.No, nor under addition, either. The sum or difference of two odd numbers is NOT an odd number.

Arithmetic is the process of applying the four basic operations: addition, subtraction, multiplication and division to numbers.

A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .

They are closed under all except that division by zero is not defined.

Whole numbers subtraction: YesDivision integers: No.

Irrational numbers are not closed under any of the fundamental operations. You can always find cases where you add two irrational numbers (for example), and get a rational result. On the other hand, the set of real numbers (which includes both rational and irrational numbers) is closed under addition, subtraction, and multiplication - and if you exclude the zero, 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.

To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.

A set is closed under a particular operation (like division, addition, subtraction, etc) if whenever two elements of the set are combined by the operation, the answer is always an element of the original set. Examples: I) The positive integers are closed under addition, because adding any two positive integers gives another positive integer. II) The integers are notclosed under division, because it is not true that an integer divided by an integer is an integer (as in the case of 1 divided by 5, for example). In this case, the answer depends on the definition of "whole numbers". If this term is taken to mean positive whole numbers (1, 2, 3, ...), then the answer is no, they are not closed under subtraction, because it is possible to subtract two positive whole numbers and get an answer that is not a positive whole number (as in the case of 1 - 10 = -9, which is not a positive whole number)

Subtraction.

Yes, they are.

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.

The set of even numbers is closed under addition, the set of odd numbers is not.