Even when one claims that she had never heard the term set before, it is more than sure that she has used the notion of a set many times in her everyday life. For instance, when we talk about a flock seagulls, a herd of elephants, or a swarm of bees we actually talk about sets. Roughly, we could say that a set is a collection, a group, but not a class of things, animals, or, more generally, objects. In general, it is not easy or even possible to get more specific. Nevertheless, it should be obvious that all objects that make up a set should be of the same kind. But what is so special about classes that prohibits their use in then “definition” of sets? The answer is simple: This term a precise technical meaning in mathematics, so it is best to avoid using this term when talking about sets.

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A Précis of Basic Set Theory

  • Apostolos Syropoulos

摘要

Even when one claims that she had never heard the term set before, it is more than sure that she has used the notion of a set many times in her everyday life. For instance, when we talk about a flock seagulls, a herd of elephants, or a swarm of bees we actually talk about sets. Roughly, we could say that a set is a collection, a group, but not a class of things, animals, or, more generally, objects. In general, it is not easy or even possible to get more specific. Nevertheless, it should be obvious that all objects that make up a set should be of the same kind. But what is so special about classes that prohibits their use in then “definition” of sets? The answer is simple: This term a precise technical meaning in mathematics, so it is best to avoid using this term when talking about sets.