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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.
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.
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.
What do you mean by 'whole number are closed under addition'?
The sum of any two whole numbers is a whole number.
Can b be a decimal number if a is a whole number?
Yes, because if A is your whole, B should be your decimal
Why do whole number require an extension?
The set of whole numbers is not closed under division (by non-zero whole numbers).
Is the difference between whole numbers always a whole number?
Difference of two whole number is not always a whole number.For any two whole numbers a & b, a - b = whole number only when a is greater than or equal to b.* * * * *Wrong!Even if a is less than b, the difference is still a whole number. Whole numbers can be negative.So the correct answer to the question is "YES".
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.
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.
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.
Is a whole number rational number?
Yes. A rational number is one that you can write as a fraction a/b, with integers a and b (b not equal to zero). For a whole number, set b = 1. For example, 5 = 5/1, so it is a rational number.
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.
