Abstract
This chapter contains a brief introduction to set theory which is essential for doing mathematics. There are two main axiomatic systems to introduce sets, viz. Zermelo–Fraenkel axiomatic system and the Gödel–Bernays axiomatic system. We follow the Zermelo-Fraenkel axiomatic system together with the axiom of choice.
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- 1.
In pre-axiomatic intuitive development of set theory, people took for granted that there is a set containing all sets. The argument used in the proof of the Proposition 2.1.3 led to a paradox known as ‘Russel’s paradox.’ In fact, the need for axiomatization of set theory was consequence of such paradoxes.
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Lal, R. (2017). Language of Mathematics 2 (Set Theory). In: Algebra 1. Infosys Science Foundation Series(). Springer, Singapore. https://doi.org/10.1007/978-981-10-4253-9_2
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DOI: https://doi.org/10.1007/978-981-10-4253-9_2
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Online ISBN: 978-981-10-4253-9
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