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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.
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.
WHY IS AN ODD NUMBER TIMES AN EVEN NUMBER EVEN?
Suppose m and n are integers. Then 2m+1 is an odd number and 2n is an even number.(2m + 1) * 2n = 4mn + 2n = 2*(2mn + 1). Since m and n are integers, the closure of the set of integers under multiplication and addition implies that 2mn + 1 is an integer. Thus the product is a multiple of 2: that is, it is even.
