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Set Theory | Internet Encyclopedia of Philosophy

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Set Theory is a branch of mathematics that investigates sets and their properties. The basic concepts of set theory are fairly easy to understand and appear to be self-evident. However, despite its apparent simplicity, set theory turns out to be a very sophisticated subject. In particular, mathematicians have shown that virtually all mathematical concepts and results can be formalized within the theory of sets. This is considered to be one of the greatest achievements of modern mathematics. Given this achievement, one can claim that set theory provides a foundation for mathematics. The foundational role of set theory and its mathematical development have raised many philosophical questions that have been debated since its inception in the late nineteenth century. For example, here are three: Does infinity exist, and if so, are there different kinds of infinity? Is there a mathematical universe? Are all mathematical problems solvable? Before pursuing the philosophical issues concerning

Set Theory Set Theory is a branch of mathematics that investigates sets and their properties. The basic concepts of set theory are fairly easy to understand and appear to be self-evident. However, despite its apparent simplicity, set theory turns out to be a very sophisticated subject. In particular, mathematicians have shown that virtually all mathematical concepts and results can be formalized within the theory of sets. This is considered to be one of the greatest achievements of modern mathematics. Given this achievement, one can claim that set theory provides a foundation for mathematics .

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