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Is whole numbers are closed under division?
No, whole numbers are not closed under division. It is possible to divide one whole number by another whole number and get a result which is not a whole number, for example, 1/2. One divided by two is a half.
Why is division not closed for rational numbers give an example?
If a set is closed under an operation. then the answer will be a part of that set. If you add, subtract or multiply any two rational numbers you get another national number. But when it comes to division, it is closed except for one number and that is ZERO. eg 3.56 (rational number) ÷ 0 = no answer. Since no answer is not a rational number, that rational numbers are not closed under the operation of division.
Are whole numbers closed under division?
No, whole numbers are not closed under division. When you divide one whole number by another, the result may not be a whole number. For example, dividing 1 by 2 gives 0.5, which is not a whole number. Therefore, whole numbers do not satisfy the closure property for division.
Is the set of whole numbers closed for division?
No, the result of a division of one whole number into another might be a whole number, but could also be a fraction.
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 you think that rational numbers are important?
The set of whole numbers is not closed under division by a non-zero whole number. Rational numbers provide that closure and so enable the definition of division of one integer by a non-zero integer.
Is the set of nonzero integers closed under division?
The set of nonzero integers is not closed under division. This is because dividing one nonzero integer by another can result in a non-integer. For example, ( 1 \div 2 = 0.5 ), which is not an integer. Therefore, the result of the division is not guaranteed to be a member of the set of nonzero integers.
Why are polynomials not closed under division?
Polynomials are not closed under division because dividing one polynomial by another can result in a quotient that is not a polynomial. Specifically, when a polynomial is divided by another polynomial of a higher degree, the result can be a rational function, which includes terms with variables in the denominator. For example, dividing (x^2) by (x) gives (x), a polynomial, but dividing (x) by (x^2) results in (\frac{1}{x}), which is not a polynomial. Thus, the closure property does not hold for polynomial division.
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Is the set of odd numbers closed under subtraction?
No, the set of odd numbers is not closed under subtraction. For example, if you subtract one odd number from another odd number, such as 5 - 3, the result is 2, which is an even number and not part of the set of odd numbers. Therefore, the subtraction of odd numbers can yield results that fall outside the set.
What is meaning of Quotient?
The quotient is the answer in a division problem.
Are even numbers closed under subtraction?
Yes, even numbers are closed under subtraction. When you subtract one even number from another even number, the result is always an even number. This is because both even numbers can be expressed as 2n and 2m (where n and m are integers), and their difference, 2n - 2m, can be factored as 2(n - m), which is also even.
