Question

Is the set of integers closed under the operation

Answer 1

The answer "yes" applies to addition, subtraction, and multiplication. This is because we can take any two integers and add them to get some other integer

eg: 5+7 = 12

We can subtract two integers to get some integer

eg: 9-1 = 8

And we can multiply two integers to get an integer

eg: 4*6 = 24

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The only one that isn't closed is division. We can divide some integers to get another integer

eg: 10/2 = 5

but there are cases where dividing two integers does not lead to another integer

eg: 8/5 = 1.6

The result 1.6 is not an integer since it has a decimal part

Also, the example your teacher provides has

1/6 = 0.167 approximately which is also not an integer