Foundations of Mathematics

Set Theory

What are naïve and axiomatic set theory?

The naive set theory is not one that takes everything for granted. It is actually a branch of mathematics that attempts to formalize the nature of the set using the fewest number of independent axioms possible. But it is not the answer to formalizing sets, as it quickly leads to a number of paradoxes. Because of this, mathematicians use a more formal theory called the axiomatic set theory, which is a version that uses axioms taken as uninterpreted rather than as formalization of pre-existing truths (for more about axiomatic systems, see elsewhere in this chapter).


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