Common Mistakes Due to Mathematical Sophistry

Detalhes bibliográficos
Autor(a) principal: Silva, Cícero José da
Data de Publicação: 2022
Outros Autores: Soares, Willames de Albuquerque
Tipo de documento: Artigo
Idioma: por
Título da fonte: Research, Society and Development
Texto Completo: https://rsdjournal.org/index.php/rsd/article/view/31977
Resumo: Mathematics is present in people's daily lives, whether formally in the school or academic environment, or in places where formalities are not necessarily observed. Using mathematical concepts carelessly can generate results that do not satisfy or do not represent reality. Thus, the objective of this article was to present some sophistry in mathematics, expose some justifications and highlight the errors made in the arguments. From basic expressions, known to a large part of the students, it was demonstrated how to obtain mathematical absurdities. Some resolutions presented were used, generally by students who do not pay attention to the definitions and hypotheses necessary for their correct applications. Also a theorem has been created that affirms the obvious. Thus, it can be concluded that when using invalid mathematical arguments in a demonstration or application, such as those that violate axioms, logical arguments, definitions or hypotheses, it is possible to deduce contradictions or frightening results, which can bring surprises.
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spelling Common Mistakes Due to Mathematical SophistryErrores Comunes Debido a la Sofística MatemáticaErros Comuns Decorrentes de Sofismas MatemáticosMathematical expressionsEducation formalFallacies.Expresiones matemáticasEducaciónFalacias.Expressões matemáticasFormal educação formalFalácias.Mathematics is present in people's daily lives, whether formally in the school or academic environment, or in places where formalities are not necessarily observed. Using mathematical concepts carelessly can generate results that do not satisfy or do not represent reality. Thus, the objective of this article was to present some sophistry in mathematics, expose some justifications and highlight the errors made in the arguments. From basic expressions, known to a large part of the students, it was demonstrated how to obtain mathematical absurdities. Some resolutions presented were used, generally by students who do not pay attention to the definitions and hypotheses necessary for their correct applications. Also a theorem has been created that affirms the obvious. Thus, it can be concluded that when using invalid mathematical arguments in a demonstration or application, such as those that violate axioms, logical arguments, definitions or hypotheses, it is possible to deduce contradictions or frightening results, which can bring surprises.Las matemáticas están presentes en la vida cotidiana de las personas, ya sea formalmente en el ámbito escolar o académico, o en lugares donde no necesariamente se observan formalidades. Usar conceptos matemáticos sin cuidado puede generar resultados que no satisfacen o no representan la realidad. Así, el objetivo de este artículo fue presentar algunos sofismas en matemáticas, exponer algunas justificaciones y resaltar los errores cometidos en los argumentos. A partir de expresiones básicas, conocidas por gran parte de los alumnos, se demostró cómo obtener absurdos matemáticos. Algunas resoluciones presentadas fueron utilizadas, generalmente por estudiantes que no prestan atención a las definiciones e hipótesis necesarias para su correcta aplicación. También se ha creado un teorema que afirma lo obvio. Así, se puede concluir que al utilizar argumentos matemáticos inválidos en una demostración o aplicación, como aquellos que violan axiomas, argumentos lógicos, definiciones o hipótesis, es posible deducir contradicciones o resultados espantosos, que pueden traer sorpresas.A matemática está presente no cotidiano das pessoas, seja formalmente no ambiente escolar ou acadêmico, ou em locais onde as formalidades não são necessariamente observadas. Utilizar os conceitos matemáticos de forma desatenta, podem gerar resultados que não satisfazem ou que não representam a realidade. Desta forma, o objetivo desse artigo foi apresentar alguns sofismas na matemática, expor algumas justificativas e evidenciar os erros cometidos nas argumentações. A partir de expressões básicas, conhecidas por uma grande parte dos estudantes, demonstrou-se como se pode obter absurdos matemáticos. Utilizou-se algumas resoluções apresentadas, geralmente por alunos que não se atentam as definições e hipóteses necessárias para as suas corretas aplicações. Também se criou um teorema que afirma o obvio. Assim, pode-se concluir que ao utilizar argumentos matemáticos não válidos em uma demonstração ou aplicação, tais como aqueles que ferem axiomas, argumentos lógicos, definições ou hipóteses, é possível deduzir contradições ou resultados assustadores, que podem trazer surpresas.Research, Society and Development2022-07-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://rsdjournal.org/index.php/rsd/article/view/3197710.33448/rsd-v11i9.31977Research, Society and Development; Vol. 11 No. 9; e21711931977Research, Society and Development; Vol. 11 Núm. 9; e21711931977Research, Society and Development; v. 11 n. 9; e217119319772525-3409reponame:Research, Society and Developmentinstname:Universidade Federal de Itajubá (UNIFEI)instacron:UNIFEIporhttps://rsdjournal.org/index.php/rsd/article/view/31977/27071Copyright (c) 2022 Cícero José da Silva; Willames de Albuquerque Soareshttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessSilva, Cícero José da Soares, Willames de Albuquerque 2022-07-21T12:36:16Zoai:ojs.pkp.sfu.ca:article/31977Revistahttps://rsdjournal.org/index.php/rsd/indexPUBhttps://rsdjournal.org/index.php/rsd/oairsd.articles@gmail.com2525-34092525-3409opendoar:2024-01-17T09:48:07.456705Research, Society and Development - Universidade Federal de Itajubá (UNIFEI)false
dc.title.none.fl_str_mv Common Mistakes Due to Mathematical Sophistry
Errores Comunes Debido a la Sofística Matemática
Erros Comuns Decorrentes de Sofismas Matemáticos
title Common Mistakes Due to Mathematical Sophistry
spellingShingle Common Mistakes Due to Mathematical Sophistry
Silva, Cícero José da
Mathematical expressions
Education formal
Fallacies.
Expresiones matemáticas
Educación
Falacias.
Expressões matemáticas
Formal educação formal
Falácias.
title_short Common Mistakes Due to Mathematical Sophistry
title_full Common Mistakes Due to Mathematical Sophistry
title_fullStr Common Mistakes Due to Mathematical Sophistry
title_full_unstemmed Common Mistakes Due to Mathematical Sophistry
title_sort Common Mistakes Due to Mathematical Sophistry
author Silva, Cícero José da
author_facet Silva, Cícero José da
Soares, Willames de Albuquerque
author_role author
author2 Soares, Willames de Albuquerque
author2_role author
dc.contributor.author.fl_str_mv Silva, Cícero José da
Soares, Willames de Albuquerque
dc.subject.por.fl_str_mv Mathematical expressions
Education formal
Fallacies.
Expresiones matemáticas
Educación
Falacias.
Expressões matemáticas
Formal educação formal
Falácias.
topic Mathematical expressions
Education formal
Fallacies.
Expresiones matemáticas
Educación
Falacias.
Expressões matemáticas
Formal educação formal
Falácias.
description Mathematics is present in people's daily lives, whether formally in the school or academic environment, or in places where formalities are not necessarily observed. Using mathematical concepts carelessly can generate results that do not satisfy or do not represent reality. Thus, the objective of this article was to present some sophistry in mathematics, expose some justifications and highlight the errors made in the arguments. From basic expressions, known to a large part of the students, it was demonstrated how to obtain mathematical absurdities. Some resolutions presented were used, generally by students who do not pay attention to the definitions and hypotheses necessary for their correct applications. Also a theorem has been created that affirms the obvious. Thus, it can be concluded that when using invalid mathematical arguments in a demonstration or application, such as those that violate axioms, logical arguments, definitions or hypotheses, it is possible to deduce contradictions or frightening results, which can bring surprises.
publishDate 2022
dc.date.none.fl_str_mv 2022-07-07
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://rsdjournal.org/index.php/rsd/article/view/31977
10.33448/rsd-v11i9.31977
url https://rsdjournal.org/index.php/rsd/article/view/31977
identifier_str_mv 10.33448/rsd-v11i9.31977
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv https://rsdjournal.org/index.php/rsd/article/view/31977/27071
dc.rights.driver.fl_str_mv Copyright (c) 2022 Cícero José da Silva; Willames de Albuquerque Soares
https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2022 Cícero José da Silva; Willames de Albuquerque Soares
https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Research, Society and Development
publisher.none.fl_str_mv Research, Society and Development
dc.source.none.fl_str_mv Research, Society and Development; Vol. 11 No. 9; e21711931977
Research, Society and Development; Vol. 11 Núm. 9; e21711931977
Research, Society and Development; v. 11 n. 9; e21711931977
2525-3409
reponame:Research, Society and Development
instname:Universidade Federal de Itajubá (UNIFEI)
instacron:UNIFEI
instname_str Universidade Federal de Itajubá (UNIFEI)
instacron_str UNIFEI
institution UNIFEI
reponame_str Research, Society and Development
collection Research, Society and Development
repository.name.fl_str_mv Research, Society and Development - Universidade Federal de Itajubá (UNIFEI)
repository.mail.fl_str_mv rsd.articles@gmail.com
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