Informalset

Informalset is a term used in mathematics, particularly in set theory, to describe a collection of objects that may not be well-defined or rigorously specified. Unlike formal sets, where membership criteria are precise and unambiguous, informal sets allow for a looser interpretation of what constitutes an element. This concept often arises in contexts where the precise boundaries of a collection are not crucial for the immediate discussion or when dealing with everyday language representations of groups of things.

For instance, a statement like "the set of all good books" would be considered an informal set. The criteria for "good" are subjective and vary from person to person, making it impossible to define a definitive list of elements. In contrast, a formal set would be something like "the set of all prime numbers less than 10," which clearly defines its elements as {2, 3, 5, 7}.

The use of informal sets can be practical in introductory mathematics or in fields that borrow mathematical language but do not require the strict formality of pure set theory. However, for rigorous mathematical proofs and constructions, formal sets are essential to avoid paradoxes and ensure consistency. The distinction between formal and informal sets highlights the importance of precision in mathematical definitions.