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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.
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 prime numbers closed under multiplication?
No.
Why does a rational number plus a rational number or a rational number multiplied by a rational number equal to rational number?
The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.
Are natural numbers closed under multiplication?
Yes.
Are rational numbers closed under multiplication?
Rational numbers are closed under multiplication, because if you multiply any rational number you will get a pattern. Rational numbers also have a pattern or terminatge, which is good to keep in mind.
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 rational numbers closed under multiplication?
yes
Is the set rational numbers closed under multiplication?
Yes, it is.
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.
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.
Can you add two rational numbers and get an irrational number?
No. The set of rational numbers is closed under addition (and multiplication).
Are rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
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.
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.
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.
