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If you can never, by multiplying two whole numbers, get anything but another whole number back as your answer, then, YES, the set of whole numbers must be closed under multiplication.

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6y ago
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Racquel Martin

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3y ago

Yes of course

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Q: Is the set of whole numbers are closed under multiplication?
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Is the set of whole numbers closed under subtraction?

It depends on your definition of whole numbers. The classic definition of whole numbers is the set of counting numbers and zero. In this case, the set of whole numbers is not closed under subtraction, because 3-6 = -3, and -3 is not a member of this set. However, if you use whole numbers as the set of all integers, then whole numbers would be closed under subtraction.


Do 0 and 3 have closure for addition?

A set of numbers is considered to be closed if and only if you take any 2 numbers and perform an operation on them, the answer will belong to the same set as the original numbers, than the set is closed under that operation. If you add any 2 real numbers, your answer will be a real number, so the real number set is closed under addition. If you divide any 2 whole numbers, your answer could be a repeating decimal, which is not a whole number, and is therefore not closed. As for 0 and 3, the most specific set they belong to is the whole numbers (0, 1, 2, 3...) If you add 0 and 3, your answer is 3, which is also a whole number. Therefore, yes 0 and 3 are closed under addition


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 the set of integers closed under subtraction?

yes, because an integer is a positive or negative, rational, whole number. when you subject integers, you still get a positive or negative, rational, whole number, which means that under the closure property of real numbers, the set of integers is closed under subtraction.


Is it true that no irrational numbers are whole numbers?

Yes, no irrational numbers are whole numbers.

Related questions

Is the set of whole numbers closed under multiplication?

Yes.


Are whole numbers closed under the operations of multiplication?

Yes.


Why are odd integers closed under multiplication but not under addition?

The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.


What operation are whole numbers closed under?

l think multiplication


What is the set of whole numbers closed by?

If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.


Are whole numbers closed for multiplication?

no


What is always true about whole numbers?

They form a closed set under addition, subtraction or multiplication.


Is the set of even whole numbers closed under multiplication?

Yes, it is closed. This means that if you multiply two even number, you again get a number within the set of even numbers.


Why are whole numbers closed under multiplication?

Because if X and Y are any two whole number, then X*Y is also a whole number. Always.


Are whole numbers closed with respect to multiplication?

Yes. That means that the product of two whole numbers is defined, and that it is again a whole number.


Is the set of whole numbers with 31 removed closed under the operation of multiplication?

No. Since -1 x -31 (= 31) would not be in the set.


What is an example of whole numbers are closed under division?

The whole numbers are not closed under division! The statement is false since, for example, 2/3 is not a whole number.