No. That is not how "well defined" means. It means, rather, that you can get all the information required from the given definition. Yes, a "relation", as opposed to a "function" may have many "y" values corresponding to a given "x". But such a relation is "well defined" as long as it is possible to find all y corresponding to any given x.HowToTrainYourDragon said:What exactly is the difference between saying a relation is well-defined vs. saying the relation is a function? Since a relation is well-defined iff each element of the domain is mapped to exactly one element in the codomain, aren't well-defined and function basically the same thing?
The term "well-defined" refers to a concept or statement that is clear, precise, and unambiguous. It is commonly used in mathematics and other scientific fields to describe an idea or theory that can be easily defined and understood.
A concept is considered to be "well-defined" if it is logically consistent and does not contain any contradictions or ambiguities. This means that it can be defined and understood in a specific and consistent manner, without any room for interpretation.
Using "well-defined" concepts in science allows for more accurate and reliable results. It ensures that everyone in the scientific community understands and uses the same definitions, reducing the potential for miscommunication or misunderstandings. It also allows for easier replication of experiments and theories.
No, a concept that is subjective is not considered to be "well-defined" as it is based on personal opinions or perspectives. In science, concepts should be objective and based on empirical evidence and logical reasoning.
To ensure that a concept is "well-defined," it is important to carefully define its terms and assumptions, and to test it through experiments and observations. Peer review and critical analysis by other scientists can also help to refine and clarify any potential ambiguities or contradictions.