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.
Lobectomy
A character that is well developed & clearly defined in a story with much detail.
A character that is well developed & clearly defined in a story with much detail.
Alopecia areata.
well defined
A well-defined set has clear and unambiguous criteria for its membership, meaning that it is possible to determine whether any given element belongs to the set. For example, the set of all even numbers is well-defined because it follows a specific rule. In contrast, a not well-defined set lacks clear criteria, making it difficult to determine which elements belong to it; for instance, a set described as "all interesting things" is subjective and varies from person to person.
A defined chin typically refers to a well-defined, prominent, and sculpted chin that enhances the overall symmetry and structure of the face. This feature can create a more balanced profile and is often considered aesthetically pleasing.
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.
well-defined sets are sets that can identify easily while not well-defined are those that cannot determined easily :)
In mathematics, a well-defined concept refers to an object, operation, or statement that is clear and unambiguous, meaning it can be consistently understood and applied within a given context. For example, a well-defined function assigns exactly one output for each input from its domain. This clarity ensures that mathematicians can communicate ideas effectively and that results can be reliably reproduced and built upon. If a concept is not well-defined, it can lead to confusion and misinterpretation.
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.
A well-defined set is a collection of distinct objects or elements that can be clearly identified and specified based on a specific criterion or property. Each member of the set can be determined without ambiguity, meaning that it is clear whether an object belongs to the set or not. For example, the set of all even integers is well-defined because there is a clear rule to identify its members. In contrast, a set defined as "nice people" is not well-defined, as the term "nice" is subjective and can vary from person to person.