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Is the set of rational numbers closed under division and Why?
No. Zero is a rational number, but division by zero is not defined.
Are integers closed under division?
No. Integers are not closed under division because they consist of negative and positive whole numbers. NO FRACTIONS!No.For a set to be closed under an operation, the result of the operation on any members of the set must be a member of the set.When the integer one (1) is divided by the integer four (4) the result is not an integer (1/4 = 0.25) and so not member of the set; thus integers are not closed under division.
Why do whole number require an extension?
The set of whole numbers is not closed under division (by non-zero whole numbers).
What does closed under division mean?
When you will divide any element in the set by another element in the set the result will be an answer that is also included in the set.
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.
Is 1 a set closed under division?
yes
What does this mean Which set of these numbers 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.
Are the set of rational numbers closed under division?
No, it is not. Division by zero (a rational) is not defined.
Is the set of real numbers closed under addition?
Yes. The set of real numbers is closed under addition, subtraction, multiplication. The set of real numbers without zero is closed under division.
Can you find a set of numbers that is closed under division and answer why?
-1, 1 is a set of numbers that is closed under division. The rule is if you divide among you end up with a quotient that is in the set. 1/-1 or -1/1 = -1 (-1 is in the set)
Is the set of rational numbers closed under division and Why?
No. Zero is a rational number, but division by zero is not defined.
What set of numbers is closed under division?
Integers are closed under division I think o.o. It's either counting numbers, integers or whole numbers . I cant remember :/
Are integers closed under division?
No. Integers are not closed under division because they consist of negative and positive whole numbers. NO FRACTIONS!No.For a set to be closed under an operation, the result of the operation on any members of the set must be a member of the set.When the integer one (1) is divided by the integer four (4) the result is not an integer (1/4 = 0.25) and so not member of the set; thus integers are not closed under division.
Is Division closed in Real?
No, since you can't divide by zero. On the other hand, the set of real numbers without zero is closed under division.
How are the rules for multiplication and division integers the same?
They are not the same!The set of integers is closed under multiplication but not under division.Multiplication is commutative, division is not.Multiplication is associative, division is not.
Why are rational numbers not like integers?
The set of rational numbers is closed under division, the set of integers is not.
Why do whole number require an extension?
The set of whole numbers is not closed under division (by non-zero whole numbers).
