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What does it mean for a set to be "closed"?

1 An expression belonging to a closed set cannot be used to create an expression that is not of that set.

2 Members of a closed set cannot be added, subtracted, multiplied, or divided.

3 An operation performed on members of that set will result in a member of the same set.

4 The set has a finite number of members, as opposed to being infinitely large.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

The correct interpretation of what it means for a set to be "closed" is:

**3. An operation performed on members of that set will result in a member of the same set.**

In mathematical terms, a set is said to be closed under a particular operation (such as addition, subtraction, multiplication, or division) if performing that operation on members of the set always yields a result that is also a member of the set.

For example:
- The set of even integers is closed under addition, because the sum of any two even integers is also an even integer.
- The set of natural numbers is not closed under subtraction, because subtracting two natural numbers can yield a negative number, which is not a natural number.

The other statements do not accurately describe the concept of a closed set in this context.