Question

Can you check this? Under what operations are the set of integers closed? Explain your answer.

I put: It's closed under addition and subtraction.
Addition: Real Number + Real Number = Real Number (closed)
Subtraction: Set of rational numbers (closed)

Is that right?

Answer 1

The posted question is about closure of the set of Integers under operations. Yet, your examples mention Real numbers and Rational numbers.

What is the original question?

Answer 2

Question: Is the set of Integers closed under the operation of multiplication?

If you pick any two integers and multiply them, will the product also be an integer?

@haileemackk

Answer 3

Sorry, I left my computer. The original question was "Under what operations are the set of integers closed? Explain your answer."

What I meant was "Integers are closed under addition and subtraction."

Would multiplication be closed too since it would still be an integer? But if multiplication was closed because of the integer, wouldn't division be too?

Answer 4

It's also closed under multiplication as well.

Answer 5

It isn't closed under division.

Answer 6

The definition of a rational number is division between two integers.

Answer 7

The original question was "Under what operations are the set of integers closed?

"Integers are closed under addition and subtraction." Would multiplication be closed too since the product would still be an integer? YES.

Regarding division, a question:

2 is an Integer, 3 is an Integer. Is 2 divided by 3 an integer? @haileemackk

Answer 8

While you are cogitating on that, I am uploading a number family tree for use later on.

Answer 9

Oh okay, I see what you mean. 2/3 would be 0.6666 so it's not an integer, but the others are since they are whole numbers.

Thanks for the sheet, the one I have isn't as helpful!

Answer 10

@haileemackk Let's practice.

Given the operations of addition, subtraction, multiplication, and division, under which of these is the set of Rational numbers closed?