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The sum of any two whole numbers is a whole number.
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∙ 12y ago
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Are whole numbers closed under the operations of addition?
Yes. When you add any whole numbers you get another whole number. That is what closed means in this context. The answer is still a whole number.
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.
Are the whole numbers closed under addition?
Yes.
What is an example of a counterexample for the difference of two whole numbers is a whole number?
There is no counterexample because the set of whole numbers is closed under addition (and subtraction).
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.
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
Are whole numbers closed under addition?
certainly - the sum of two whole nos. is again a whole no.
Are the whole numbers closed under addition if so explain?
Yes because being closed under an operation means that when the operation is performed on members of a set the result is also a member of the set, and when any two [members of the set of] whole numbers are added together the result of the addition is also a whole number which is, unsurprisingly, a member of the set of whole numbers.
What is the number of protons plus the number of neutrons in an atom always a whole number?
The two are counts and so natural numbers. The set of natural numbers is closed under addition.
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 do whole number require an extension?
The set of whole numbers is not closed under division (by non-zero whole numbers).
Why is the answer always a whole number when the sum of two digits under 10 are added together?
This follows from the property that the set of integers is closed under addition. This means that any two integers, when added together, must always result in a whole number.
