What are closed sets and not closed sets?

well, I’m having a pretty difficult time understanding this.

Sets Operation

{1,2,3,…} subtraction

Help me out here, and give me an example of a closed sets and not closed sets. ( simple examples please)

Top 1 Answers

A few days ago

TurtleFromQuebec

Favorite Answer

A set of numbers is closed under an operation if applying the operation to two numbers in the set will always give another number that’s in the set.

For example, {1,2,3,…}, the set of whole numbers bigger than 0, is closed under addition, because adding any two whole numbers bigger than 0 will always give another whole number bigger than 0. You’ll never get 0 or a negative number or a fraction.

But {1,2,3,…} is NOT closed under subtraction. For example,. 1 – 2 is a negative number, and there are no negative numbers in the set. Even 3 – 3 gives 0, which is not in the set.

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