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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 all even integers closed with respect to multiplication?
Yes, it is.
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.
What are the characteristics of integers?
Integers are the natural numbers (counting numbers: 1,2,3,etc.), and their negative counterparts, and zero. The set of Integers is closed for addition, subtraction, and multiplication, but not division. Closed means that the answer will be a part of the set. Example: 1/3 (1 divided by 3 equals one third) is not an integer, even though both 1 and 3 are integers.
Is the set of irrational numbers a group under the operation of multiplication?
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
Is the set of even integers closed under addition and multiplication?
Yes.
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.
Are any of these sets closed under multiplication?
To determine if a set is closed under multiplication, we need to check if the product of any two elements from the set is also an element of the same set. For example, the set of integers is closed under multiplication because the product of any two integers is always an integer. In contrast, the set of natural numbers is also closed under multiplication, while the set of rational numbers is closed under multiplication as well. However, sets like the set of positive integers and the set of even integers are also closed under multiplication.
Is the set of all even integers closed with respect to multiplication?
Yes, it is.
Is the product of an even number and an even number closed under multiplication?
Yes.
Does the set of even integers form a group under the operation of multiplication?
No. The inverses do not belong to the group.
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.
What are the characteristics of integers?
Integers are the natural numbers (counting numbers: 1,2,3,etc.), and their negative counterparts, and zero. The set of Integers is closed for addition, subtraction, and multiplication, but not division. Closed means that the answer will be a part of the set. Example: 1/3 (1 divided by 3 equals one third) is not an integer, even though both 1 and 3 are integers.
Is the set of even integers closed under subtraction and division?
Subtraction: Yes. Division: No. 2/4 = is not an integer, let alone an even integer.
Is the set of irrational numbers a group under the operation of multiplication?
No. It is not even closed. sqrt(3)*sqrt(3) = 3 - which is rational.
Is the set of all even integers closed with respect to addition?
Yes, it is.
Is multiplication of a whole number associative?
Yes. Multiplication of integers, of rational numbers, of real numbers, and even of complex numbers, is both commutative and associative.
