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No. One of the group axioms is that each element must have an inverse element. This is not the case with integers. In other words, you can't solve an equation like:
5 times "n" = 1
in the set of integers.
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Is the set of even integers closed under multiplication?
Yes
Why is a set of positive integers not a group under the operation of addition?
The set of positive integers does not contain the additive inverses of all but the identity. It is, therefore, not a group.
Is the set of all negative integers a group under addition?
no
Which set is closed under the operation multiplication?
Any set where the result of the multiplication of any two members of the set is also a member of the set. Well known examples are: the natural numbers (ℕ), the integers (ℤ), the rational numbers (ℚ), the real numbers (ℝ) and the complex numbers (ℂ) - all closed under multiplication.
Is the set of positive integers a field under addition and multiplication?
NO. Certainly not. Additive inverse and Multiplicative inverse doesn't exist for many elements.
Is the set of all integers a group under multiplication?
No. The set does not include inverses.
Does the set of even integers form a group under the operation of multiplication?
No. The inverses do not belong to the group.
Example of group is an abelian group?
The set of integers, under addition.
Is set of integers is a field?
The set of integers is not closed under multiplication and so is not a field.
Is set of integers closed under multiplication?
Yes!
Is the set of integers closed under multiplication?
Yes!
Is the set of even integers closed under multiplication?
Yes
How are the rules for multiplication and division integers the same?
They are not the same!The set of integers is closed under multiplication but not under division.Multiplication is commutative, division is not.Multiplication is associative, division is not.
Is the set of all integers closed under the operation of multiplication?
Yes.
Is the set of even integers closed under addition and multiplication?
Yes.
Is the set of negative integers closed under multiplication real numbers?
No, it is not.
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.
