Kuratowski-Zorn lemma in High Scholl mathematics
Keywords:Zorn's lemma; Set theory; Linear algebra; Axiom of choice.
Zorn's lemma has been the subject of controversy and debate since its emergence, despite its relevance can be perceived by the large number of applications and consequences presented on the form of equivalent statements that are present in the area of exact, and also in mathematical applications that they are based on the set theory as, axiom of Choice, Theorem of Good Order, Tychonoff's Theorem, Hahn Banach Theorem among others, the first three being equivalent to Zorn's Lemma. For this reason, we will aim, starting from a historical approach on the same, to present one of the applications that are responsible for strengthening its notoriety and popularity among mathematical scholars and scientists from the most varied areas that use Linear Algebra to represent and solve their problems. mathematical models using this lemma and its equivalences, where we will see how we can find it in the mathematics of regular high school schools when presented to students.
Beth, E (1964) The Foundations of Mathematics: A Study in the Philosophy of Science rev. ed. Harper Torchbooks.
Boccato, V. R. C. (2006) Metodologia da pesquisa bibliográfica na área odontológica e o artigo científico como forma de comunicação. Rev. Odontol. Univ. Cidade São Paulo, 18(3).
Celestino, R. (2000). Ensino-Aprendizagem da Álgebra linear: As pesquisas brasileiras na década de 90. (Dissertação de Mestrado, PUC-SP)
Campbell, P. J. (1978). The origin of Zorn’s Lemma.Historia Mathematica. 77 (85), 77-89.
Cuesta, N 1955 Injusta atribucidn a Zorn de1 principio maximal Gac. Mat. (Madrid) (1) 7, 174-176 (MR 17, 931)
Diniz, M (2019). Teoria dos conjuntos: Sim ou Não? http://mathema.com.br/reﬂexoes/teoria-dos-conjuntos-sim-ou-nao-2/.
Fraenkel, A. A. & Bar-Hillel, Y. (1958) Foundations of Set Theory Amsterdam (North-Holland) (MR 21, #648)
Grace, A. K. S. G. S. (2010). Inﬁnitos, Contínuos e Escolha: Teoria dos Conjuntos. (Dissertação de Conclusão de Curso, Universidade Federal de São Carlos)
Halmos, P. R. H. R. (2001). Teoria Ingênua dos Conjuntos. Editora Ciência Moderna.
Jech, T. J. (1973). The Axiom of Choice Amsterdam (North- Holland)
Lipschutz, S (1972). Teoria dos Conjuntos. McGraw-Hill Ltda.
Pereira, A. C. C.& Saito, F. (2018). Os instrumentos matemáticos na interface entre história e ensino de matemática: compreendendo o cenário nacional nos últimos 10 anos. Boletim Cearense de Educação e História da Matemática, 5(14).
Rubin, H & Rubin, J. R. H. (1963). Equivalents of the Axiom of choice. Noth-Holland Publishing company-Amsterdam.
Semadeni, Z. (1968) Notes to J. Mikusifiski's article "On Zorn's theorem" (Polish) Wiadom. Mat. (2) 10, 145-146 (MR 39, #1273) (Passages quoted were translated by the author, with the assistance of Ann E. Lynch)
Silva, S. G., & Jesus, J. P. C. (2007). Cem anos do axioma de escolha. Revista Matemática Universitária n◦42.
Suppes, P. (1960) Axiomatic Set Theory Princeton (Van Nostrand)
How to Cite
Copyright (c) 2021 Eduardo da Conceição Rosário; Cassio Alessandro Batista Balieiro; Neylan Leal Dias; Simone de Almeida Delphim Leal
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
1) Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2) Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3) Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.