## When is a set closed under particular arithmetic operation?

Sequences, counting (including probability), logic and truth tables, algorithms, number theory, set theory, etc.
georgiepeorgie
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### When is a set closed under particular arithmetic operation?

When is a set closed under a particular arithmetic operation?
This makes absolutely no sense to me! Any input would be great!

stapel_eliz
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For a set to be "closed" under a given operation, it must be that the results of that operation are always within the set.

For instance, the even numbers are closed under addition, since the sum of any two even numbers is another even number. On the other hand, the odd numbers are not closed under addition, since the sum of any two odd numbers is not another odd number, but an even number. Since this operational result is outside of the set, then the set is not closed under the operation.

Hope that helps a bit!