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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.
What else can I help you with?
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 rational numbers closed under multiplication?
yes
Is the set of even integers 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.
Are any of these sets closed under multiplication?
To determine if a set is closed under multiplication, we need to check if the product of any two elements from the set is also an element of the same set. For example, the set of integers is closed under multiplication because the product of any two integers is always an integer. In contrast, the set of natural numbers is also closed under multiplication, while the set of rational numbers is closed under multiplication as well. However, sets like the set of positive integers and the set of even integers are also closed under multiplication.
Are the integers closed under multiplication?
Yes, the integers are closed under multiplication. This means that when you multiply any two integers together, the result is always an integer. For example, multiplying -3 and 4 yields -12, which is also an integer. Therefore, the set of integers is closed under the operation of multiplication.
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 the set of integers closed under multiplication?
Yes!
Is set of integers closed under multiplication?
Yes!
Is this set of negative numbers closed under multiplication or addition?
Yes. The empty set is closed under the two operations.
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).
