0
Is a set of negative numbers closed under the operation of taking the absolute value?
Wiki User
∙ 11y ago
Well, the negatives would become positives because they're in between the absolute value. (| |).
For an example:
| 5 - 2 + 13- 3|
Would become
|5+ -2 + 13 + -3|
then if you add them, you get
|3 + 10|
and 10 + 3 is |13| which becomes 13.
So basically, any equation in the absolute value will be positive, unless there's a negative sign on the outside of the symbol. Like this for an example, would be negative:
-|5+ 3+10|
Add them and you get:
-|18|
take the absolute value off, and you get a -18.
Wiki User
∙ 11y ago
Add your answer:
Earn +20 pts
Is the set of all negative numbers closed under the operation of multiplication Explain why or why not?
No. For a set to be closed with respect to an operation, the result of applying the operation to any elements of the set also must be in the set. The set of negative numbers is not closed under multiplication because, for example (-1)*(-2)=2. In that example, we multiplied two numbers that were in the set (negative numbers) and the product was not in the set (it is a positive number). On the other hand, the set of all negative numbers is closed under the operation of addition because the sum of any two negative numbers is a negatoive number.
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.
When is a set of negative irrational numbers closed?
It cannot be closed under the four basic operations (addition, subtraction, multiplication, division) because it is indeed possible to come up with two negative irrational numbers such that their sum/difference/product/quotient is a rational number, indicating that the set is not closed. You will have to think of a different operation.
Is the set of all negative integers closed for operation of addition?
yes
Are natural numbers closed under the operation of multiplicaton?
yes
What is an counterexample of the set of negative integers is closed under the operation of taking the absolute value?
-3 is a negative integer. The absolute value of -3 is +3 which is not a negative integer. So the set is not closed.
Is the set of all negative numbers closed under the operation of multiplication Explain why or why not?
No. For a set to be closed with respect to an operation, the result of applying the operation to any elements of the set also must be in the set. The set of negative numbers is not closed under multiplication because, for example (-1)*(-2)=2. In that example, we multiplied two numbers that were in the set (negative numbers) and the product was not in the set (it is a positive number). On the other hand, the set of all negative numbers is closed under the operation of addition because the sum of any two negative numbers is a negatoive number.
Is the set of all negative numbers closed under the operation of multiplication explain why or why?
No.When you multiply two negative numbers together, you do not get a negative number as the answer.
Are real numbers closed under the square root operation?
No. Negative numbers are real but their square roots are not.
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.
When is a set of negative irrational numbers closed?
It cannot be closed under the four basic operations (addition, subtraction, multiplication, division) because it is indeed possible to come up with two negative irrational numbers such that their sum/difference/product/quotient is a rational number, indicating that the set is not closed. You will have to think of a different operation.
Under which operation are natural numbers closed?
Addition.
Why is zero not closed under the operation of whole numbers?
A set can be closed or not closed, not an individual element, such as zero. Furthermore, closure depends on the operation under consideration.
Is the set of all negative integers closed for operation of addition?
yes
Are natural numbers closed under the operation of multiplicaton?
yes
Are rational numbers closed under subtraction operation?
Yes, they are.
Is set of numbers closed under natural and subtraction?
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.
