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What does it mean for a set to be "closed"?
Responses
An expression belonging to a closed set cannot be used to create an expression that is not of that set.
An expression belonging to a closed set cannot be used to create an expression that is not of that set.
The set has a finite number of members, as opposed to being infinitely large.
The set has a finite number of members, as opposed to being infinitely large.
Members of a closed set cannot be added, subtracted, multiplied, or divided.
Members of a closed set cannot be added, subtracted, multiplied, or divided.
An operation performed on members of that set will result in a member of the same set.
Responses
An expression belonging to a closed set cannot be used to create an expression that is not of that set.
An expression belonging to a closed set cannot be used to create an expression that is not of that set.
The set has a finite number of members, as opposed to being infinitely large.
The set has a finite number of members, as opposed to being infinitely large.
Members of a closed set cannot be added, subtracted, multiplied, or divided.
Members of a closed set cannot be added, subtracted, multiplied, or divided.
An operation performed on members of that set will result in a member of the same set.
Answers
Answered by
GPT-4o mini
The correct definition of a "closed" set, particularly in the context of mathematics and operations, is that:
**An operation performed on members of that set will result in a member of the same set.**
This means that if you take any two elements from a closed set and perform a specific operation (like addition, multiplication, etc.), the result will also be an element of the same set. For example, the set of integers is closed under addition because the sum of any two integers is an integer.
The other statements provided do not accurately describe the concept of a closed set in mathematical terms. A closed set can be finite or infinite, and members of a closed set can be operated on in certain ways while still remaining within the set, depending on the operation and the specific set in question.
**An operation performed on members of that set will result in a member of the same set.**
This means that if you take any two elements from a closed set and perform a specific operation (like addition, multiplication, etc.), the result will also be an element of the same set. For example, the set of integers is closed under addition because the sum of any two integers is an integer.
The other statements provided do not accurately describe the concept of a closed set in mathematical terms. A closed set can be finite or infinite, and members of a closed set can be operated on in certain ways while still remaining within the set, depending on the operation and the specific set in question.
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