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Is the set of happy people not well defined?
Yes, the set of happy people is not well defined.
Is the set of big people not well defined?
It can only become well defined when you specify what constitutes a big person. Is it over 1.8 metres for example, or over 125 kg? or some other measure.
is the set of big people well defined or not and why?
No, the set of big people is not well defined. For example, small children tend to call all adults "big people", even Jerry's Mom, who is only 4'10" tall and weighs 98 lbs. But when Jerry's Mom goes to church, she is the smallest adult there, so she is not considered a big person. Also, when you say big person, does that refer to height or could it also refer to girth? Is a 5'2" person weighing 250 lbs. a big person?
What is the well defined set?
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.
What is the meaning of well-defined set?
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.
