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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 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 always true about whole numbers?
They form a closed set under addition, subtraction or multiplication.
Why is zero not closed under the operation of whole numbers?
A set can be closed or not closed, not an individual element, such as zero. Furthermore, closure depends on the operation under consideration.
Why do whole numbers need an extension?
The first need arose when it was found that the set of whole numbers was not closed under division. That is, given whole numbers A and B (B non-zero), that, in general, A/B was not a whole number - but a fraction.
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.
Why do whole number require an extension?
The set of whole numbers is not closed under division (by non-zero whole numbers).
Is the set of whole numbers are closed under multiplication?
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.
Why is the set of positive whole numbers closed under subtraction?
The set of positive whole numbers is not closed under subtraction! In order for a set of numbers to be closed under some operation would mean that if you take any two elements of that set and use the operation the resulting "answer" would also be in the original set.26 is a positive whole number.40 is a positive whole number.However 26-40 = -14 which is clearly not a positive whole number. So positive whole numbers are not closed under subtraction.
Is the set of whole numbers closed under multiplication?
Yes.
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 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).
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.
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
What is the principle of closure math?
When you combine any two numbers in a set the result is also in that set. e.g. The set of whole numbers is closed with respect to addition, subtraction and multiplication. i.e. when you add, subtract or multiply two numbers the answer will always be a whole number. But the set of whole numbers is NOT closed with respect to division as the answer is not always a whole number e.g. 7÷5=1.4 The answer is not a whole number.
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 :/
What is always true about whole numbers?
They form a closed set under addition, subtraction or multiplication.
