Here's a breakdown of why there isn't a fixed list of 464 definitions:
* Different Perspectives: Set theory has been developed in different ways by mathematicians over time. There are axiomatic approaches (like Zermelo-Fraenkel set theory), naive set theory, and different interpretations within these frameworks.
* Formal vs. Informal: The definition of "set" can be very formal and precise within axiomatic set theory, where it's defined based on a few fundamental axioms. However, in more informal contexts, "set" might simply mean "a collection of objects."
* Varying Levels of Detail: Even within a single framework, the level of detail in a definition can vary. A basic definition might say "a set is a collection of objects," while a more advanced definition might delve into the relationships between sets, subsets, and elements.
Common Ways to Define "Set":
* Informal: A set is a collection of distinct objects, called elements.
* Axiomatic: In Zermelo-Fraenkel set theory, sets are defined based on a few axioms that describe their properties and relationships.
* Intuitional: A set is a way to group together things that share a common characteristic.
Instead of looking for 464 definitions, it's more helpful to understand the different ways "set" can be defined depending on the context and purpose.