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Yes, because for any x and y that are positive fractions (y not equal to zero), x/y is also a positive fraction. Note that whole numbers are considered fractions with denominators of 1 -- otherwise it doesn't work.
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The natural numbers are closed under division?
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
True or False The set of whole numbers is closed under subtraction Why?
A set is closed under a particular operation (like division, addition, subtraction, etc) if whenever two elements of the set are combined by the operation, the answer is always an element of the original set. Examples: I) The positive integers are closed under addition, because adding any two positive integers gives another positive integer. II) The integers are notclosed under division, because it is not true that an integer divided by an integer is an integer (as in the case of 1 divided by 5, for example). In this case, the answer depends on the definition of "whole numbers". If this term is taken to mean positive whole numbers (1, 2, 3, ...), then the answer is no, they are not closed under subtraction, because it is possible to subtract two positive whole numbers and get an answer that is not a positive whole number (as in the case of 1 - 10 = -9, which is not a positive whole number)
Is 1 a set closed under division?
yes
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.
What is the counterexample for the repeating decimals are closed under division?
Division by 0, which can also be written as 0.000... (repeating) is not defined.
Are positive integers closed under division?
No, they are not.
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.
Are fractions closed under subtration?
Yes.
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 rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
Are sets of fractions closed under addition?
Yes.
Are rational numbers closed under division?
No.
The terminating decimals are closed under division?
no
Are real numbers closed under division?
no
Are fractions closed under divion by nonzero elements?
Yes.
The natural numbers are closed under division?
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
True or False The set of whole numbers is closed under subtraction Why?
A set is closed under a particular operation (like division, addition, subtraction, etc) if whenever two elements of the set are combined by the operation, the answer is always an element of the original set. Examples: I) The positive integers are closed under addition, because adding any two positive integers gives another positive integer. II) The integers are notclosed under division, because it is not true that an integer divided by an integer is an integer (as in the case of 1 divided by 5, for example). In this case, the answer depends on the definition of "whole numbers". If this term is taken to mean positive whole numbers (1, 2, 3, ...), then the answer is no, they are not closed under subtraction, because it is possible to subtract two positive whole numbers and get an answer that is not a positive whole number (as in the case of 1 - 10 = -9, which is not a positive whole number)
