User:Librarytechie2022/Infinite set

Burton, D. M. (2007). The History of Mathematics: An Introduction (Sixth ed.). Chapter 12. p 669-712. McGraw Hill.

PALA, & NARLI, S. (2020). Role of the Formal Knowledge in the Formation of the Proof Image: A Case Study in the Context of Infinite Sets. Turkish Journal of Computer and Mathematics Education, 11(3), 584–618. https://doi.org/10.16949/turkbilmat.702540

Chapter 3. Rodgers, Nancy. (2000). Learning to reason an introduction to logic, sets, and relations. Wiley.

Infinite set theory involves proofs and definitions. (Burton and Paula and Narli) Important ideas discussed by Burton include how to define "elements" or parts of a set, how to define unique elements in the set, and how to prove infinity. Burton also discusses proofs for different types of infinity, including countable and uncountable sets. Topics used when comparing infinite and finite sets include "ordered sets," "cardinality," equivalency, coordinate planes, universal sets, mapping, subsets, continuity, and "transcendence." Burton mentions that Candor's set ideas were influenced by trigonometry and irrational numbers. Other key ideas in infinite set theory mentioned by Burton, Paula, Narli and Rodger include real numbers such as pi, integers, and Euler's number.

In Chapter 12 of The History of Mathematics: An Introduction, Burton emphasizes how mathematicians such as Zermelo, Dedekind, Galileo, Kronecker, Cantor, and Bolzano investigated and influenced infinite set theory. Potential historical influences, such as how Prussia's history in the 1800's, resulted in an increase in scholarly mathematical knowledge, including Candor's theory of infinite sets.