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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.
Is the set of even integers closed under addition and multiplication?
Yes.
Is the set of negative integers is closed under addition?
No, the set of negative integers is not closed under addition. When you add two negative integers, the result is always a negative integer. However, if you add a negative integer and a positive integer, the result can be a positive integer, which is not in the set of negative integers. Thus, the set does not satisfy the closure property for addition.
Is a rational number closed under addition?
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
Is set of integers is a field?
The set of integers is not closed under multiplication and so is not a field.
ARe odd integers not closed under addition?
That is correct, the set is not closed.
Under which operation is the set of odd integers closed?
addition
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.
Is the set of even integers closed under addition and multiplication?
Yes.
What does it mean if an integer is closed?
You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).
Why the set of odd integers under addition is not a group?
Because the set is not closed under addition. If x and y are odd, then x + y is not odd.
Is the collection of integers closed under subraction?
Yes, the set of integers is closed under subtraction.
What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
Is a rational number closed under addition?
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
What does the word closure property for addition mean?
It means that given a set, if x and y are any members of the set then x+y is also a member of the set. For example, positive integers are closed under addition, but they are not closed under subtraction, since 5 and 8 are members of the set of positive integers but 5 - 8 = -3 is not a positive integer.
Is set of integers is a field?
The set of integers is not closed under multiplication and so is not a field.
Is the set of all negative integers closed for operation of addition?
yes
