answersLogoWhite

0


Best Answer

A set can be closed or not closed, not an individual element, such as zero.

Furthermore, closure depends on the operation under consideration.

User Avatar

Wiki User

โˆ™ 2013-01-16 22:38:09
This answer is:
๐Ÿ™
0
๐Ÿคจ
0
๐Ÿ˜ฎ
0
User Avatar
Study guides
๐Ÿ““
See all Study Guides
โœ๏ธ
Create a Study Guide

Add your answer:

Earn +20 pts
Q: Why is zero not closed under the operation of whole numbers?
Write your answer...
Submit
Related questions

What operation are whole numbers closed under?

l think multiplication


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.


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.


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.


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.


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 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 do whole number require an extension?

The set of whole numbers is not closed under division (by non-zero whole 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


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.


Are the whole numbers closed under addition?

Yes.


Are whole numbers closed under addition?

Yes they are.


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 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.


Is the set of whole numbers closed under multiplication?

Yes.


Are whole numbers closed under the operations of multiplication?

Yes.


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 :/


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.


Is the whole number closed under subtraction?

If you interpret "whole numbers" as "integers", then yes. If you interpret "whole numbers" as "non-negative integers", then no.


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.


What do you mean by 'whole number are closed under addition'?

The sum of any two whole numbers is a whole number.


Is the set of whole numbers closed under addition?

certainly - the sum of two whole nos. is again a whole no.


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).


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 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.