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A well defined set is one that you know exactly what is meant when you read it.

For example, the set of all people 6' 1" tall is well defined. Whenever you meet someone, if they're 6'1" tall, they're in the set. Otherwise, they're not. You know exactly what I mean. So that set is well defined.

The set of all cute shoes is not well defined. Jane just adores buckles, so any shoe with a buckle is cute to her. But Martha likes plain shoes. Buckles are big, ugly things that detract from the shoe. So a shoe with a buckle is not cute to Martha. So the set of all cute shoes is not well defined, because you can't just look at it and determine if it belongs in the set.

So the set of all buckled shoes would be well defined, but the set of all cute shoes is not.

Q: What is the well defined set?

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If there exists even one single item for which you cannot say whether it is in the set or not, the set is not well defined.

Yes, the set of happy people is not well defined.

It is a set that is well defined.

A set is a well defined collection of elements

A well defined set is one that you know exactly what is meant when you read it. For example, the set of all people 6' 1" tall is well defined. Whenever you meet someone, if they're 6'1" tall, they're in the set. Otherwise, they're not. You know exactly what I mean. So that set is well defined. The set of all cute shoes is not well defined. Jane just adores buckles, so any shoe with a buckle is cute to her. But Martha likes plain shoes. Buckles are big, ugly things that detract from the shoe. So a shoe with a buckle is not cute to Martha. So the set of all cute shoes is not well defined, because you can't just look at it and determine if it belongs in the set. So the set of all buckled shoes would be well defined, but the set of all cute shoes is not.

Related questions

Elements that have to be defined by personal judgement. Such as the set ofgreat songs is not well-defined. But the set of the English alphabet is well-defined.

Elements that have to be defined by personal judgement. Such as the set ofgreat songs is not well-defined. But the set of the English alphabet is well-defined.

its not well defined because not all the students/people like the teachers,so it is not well defined

well defined

If there exists even one single item for which you cannot say whether it is in the set or not, the set is not well defined.

Yes, the set of happy people is not well defined.

yes

It is a set that is well defined.

A set is a well defined collection of elements

its not well defined because not all the students/people like the teachers,so it is not well defined

Any well-defined set of numbers.

A well defined set is one that you know exactly what is meant when you read it. For example, the set of all people 6' 1" tall is well defined. Whenever you meet someone, if they're 6'1" tall, they're in the set. Otherwise, they're not. You know exactly what I mean. So that set is well defined. The set of all cute shoes is not well defined. Jane just adores buckles, so any shoe with a buckle is cute to her. But Martha likes plain shoes. Buckles are big, ugly things that detract from the shoe. So a shoe with a buckle is not cute to Martha. So the set of all cute shoes is not well defined, because you can't just look at it and determine if it belongs in the set. So the set of all buckled shoes would be well defined, but the set of all cute shoes is not.