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Any set where the result of the multiplication of any two members of the set is also a member of the set.
Well known examples are: the natural numbers (ℕ), the integers (ℤ), the rational numbers (ℚ), the real numbers (ℝ) and the complex numbers (ℂ) - all closed under multiplication.
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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 irrational numbers a group under the operation of multiplication?
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
What is closed under multiplication means?
A set is closed under multiplication if for any two elements, x and y, in the set, their product, x*y, is also a member of the set.
Is the set of whole numbers closed under multiplication?
Yes.
Is the set of rational numbers closed under multiplication?
yes
Is the set of all integers closed under the operation of multiplication?
Yes.
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 whole numbers with 31 removed closed under the operation of multiplication?
No. Since -1 x -31 (= 31) would not be in the set.
Is the set of composite number closed under multiplication?
Is { 0, 20 } closed under multiplication
Is the set of irrational numbers a group under the operation of multiplication?
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
What is closed under multiplication means?
A set is closed under multiplication if for any two elements, x and y, in the set, their product, x*y, is also a member of the set.
Is set of integers closed under multiplication?
Yes!
Is the set of integers closed under multiplication?
Yes!
What does it mean if an integer is closed?
You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).
Is this set of negative numbers closed under multiplication or addition?
Yes. The empty set is closed under the two operations.
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.
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.
