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Earn +20 ptsQ: Is the set of even integers closed under multiplication?
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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.
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