Q: Are real numbers closed under division?

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No, since you can't divide by zero. On the other hand, the set of real numbers without zero is closed under division.

Division, since you can't divide by zero.

The set of real numbers is closed under addition, subtraction, multiplication, and division (except that you cannot divide by zero). By closed, this means that if the two numbers in the operation are both real numbers, the result of the operation will always be a real number. Dividing by zero is undefined (for all practical purposes)

Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.

yes

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Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.

No, since you can't divide by zero. On the other hand, the set of real numbers without zero is closed under division.

It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.It means that dividing any number in the set by any other number in the set is valid, and that the result is again a member of the set.For example, the set of real numbers is NOT closed under division - you can't divide by zero.The set of real numbers, excluding zero, IS closed under division. Similarly, the set of rational numbers excluding zero is also closed under division.

Division, since you can't divide by zero.

A set of real numbers is closed under subtraction when you take two real numbers and subtract , the answer is always a real number .

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.

yes because real numbers are any number ever made and they can be closed under addition

The set of real numbers is closed under addition, subtraction, multiplication, and division (except that you cannot divide by zero). By closed, this means that if the two numbers in the operation are both real numbers, the result of the operation will always be a real number. Dividing by zero is undefined (for all practical purposes)

Yes, but only when the denominator is non-zero. Division by 0 is not defined.

Real numbers are closed under addition and subtraction. To get a number outside the real number system you would have to use square root.

No. Negative numbers are real but their square roots are not.

Yes, they are.