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Real numbers are commutative (if that is what the question means) under addition. Subtraction is a binary operation defined so that it is not commutative.

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โˆ™ 2010-04-20 13:33:31
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Q: Why are the set of real numbers is not commuted under subtraction and addition?
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Related questions

Are real numbers closed under addition and subtraction?

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


Are rational numbers closed under division multiplication addition or subtraction?

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.


Is the set of real numbers closed under addition?

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


Are rational numbers closed under subtraction?

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


Are rational numbers are closed under addition subtraction division or multiplication?

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


What is always true about whole numbers?

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


Is there a subset of the natural numbers that is closed for addition?

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.


Is the sum of rational numbers always rational?

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.


What is an example of a counterexample for the difference of two whole numbers is a whole number?

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


Are polynomial expressions closed under subtraction?

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


What is the set of whole numbers closed by?

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.


Why is it we don't have any properties of subtraction and division?

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.


Are odd numbers closed under subtraction?

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.


What is arithmetic?

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


Which set of numbers is closed under subtraction?

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


Are rational numbers are closed under addition subtraction multiplication and division?

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


Is closure exist for whole numbers under subtraction and division for integers?

Whole numbers subtraction: YesDivision integers: No.


What are irrational numbers closed under?

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.


Is the set of whole numbers closed under subtraction?

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.


Which sets of numbers are 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.


True or False The set of whole numbers is closed under subtraction Why?

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)


Under what operation is the set of positive rational numbers not closed?

Subtraction.


Are rational numbers closed under subtraction operation?

Yes, they are.


Why are odd integers closed under multiplication but not under addition?

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


What is closed and not-closed under addition?

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