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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 rational numbers closed under multiplication?
yes
Is the set of even integers closed under multiplication?
Yes
