{"data":{"id":"10.6084/m9.figshare.1572170","type":"dois","attributes":{"doi":"10.6084/m9.figshare.1572170","prefix":"10.6084","suffix":"m9.figshare.1572170","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Reis, Tiago S. Dos","nameType":"Personal","givenName":"Tiago S. Dos","familyName":"Reis","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Transmatemática"}],"publisher":"figshare","container":{},"publicationYear":2015,"subjects":[{"subject":"10301 Numerical Analysis","subjectScheme":"FOR"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"}],"contributors":[],"dates":[{"date":"2015-10-11","dateType":"Created"},{"date":"2015-10-11","dateType":"Updated"},{"date":"2015","dateType":"Issued"}],"language":null,"types":{"ris":"DATA","bibtex":"misc","citeproc":"dataset","schemaOrg":"Dataset","resourceType":"Dataset","resourceTypeGeneral":"Dataset"},"relatedIdentifiers":[],"relatedItems":[],"sizes":["711820 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"Creative Commons Attribution 4.0 International","rightsUri":"https://creativecommons.org/licenses/by/4.0/legalcode","schemeUri":"https://spdx.org/licenses/","rightsIdentifier":"cc-by-4.0","rightsIdentifierScheme":"SPDX"}],"descriptions":[{"description":"Os números transreais são uma extensão dos números reais. Este novo conjunto é fechado sob as quatro operações aritméticas: adição, subtração, multiplicação e divisão. Em particular, a divisão por zero é permitida. Neste texto, contextualizamos o leitor fazendo um resumo da concepção dos números transreais. Fazemos um apanhado histórico do desenvolvimento do conceito de número. Propomos uma construção do conjunto dos números transreais, o que demonstra a consistência de sua aritmética. Desenvolvemos o cálculo transreal, estabelecendo os conceitos de topologia, sequências, limite, continuidade, derivada e integral nos números transreais. Propomos uma semântica total, isto é, uma semântica que engloba os valores lógicos clássicos, fuzzy, de contradição e de indeterminação e definimos um espaço lógico, onde proposições e mundos possíveis são objetos matemáticos bem definidos. Desta forma, podemos definir matematicamente diversos conceitos lógicos. Como, por exemplo, relações de acessibilidade, necessidade e possibilidade, transformações lógicas e um critério pra distinguir quando uma proposição é ou não clássica. Mostramos que existe um mundo possível que pode acessar qualquer outro por aproximação. Por fim, fazemos uma discussão geral sobre a transmatemática, suas novidades e o desafio de adentrar o meio acadêmico.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://figshare.com/articles/dataset/Transmatem_tica/1572170","contentUrl":null,"metadataVersion":1,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2015-10-11T13:57:52.000Z","registered":"2015-10-11T13:57:53.000Z","published":"2015","updated":"2020-09-04T15:00:21.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.1572170","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}