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Cardona Hurtado, Oscar Abel - One of the best experts on this subject based on the ideXlab platform.
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Beneficios de la notación de Peirce para los conectivos proposicionales binarios
2016Co-Authors: Cardona Hurtado, Oscar AbelAbstract:Background: In traditional Binary Notation for propositional connectives only some of these ones are taken into account. Throughout the twentieth century several Notations were proposed which overcome this flaw, leading to the proposal of interesting mathematical problems. Objective: This paper presents the Notation created by the American Charles Peirce, showing some of the properties of this symbols, and evidencing the advantages of these compared to the traditional. Method: the Notation proposed by Peirce is described, and some properties of the geometric and algebraic logical character among its connective are verified; also, the possible role of these properties in the traditional Notation is analyzed. Results: In addition to several individual properties and multiple relations between the connectives, the symmetries of the full set of Binary propositional connective is visually evident in the signs proposed by Peirce. Conclusion: Different benefits of the Notation proposed by Peirce, support the conclusion that the usual Notation is clearly surpassed by the symbolism designed by the American scientist.Antecedentes: Na notação tradicional para os conectivos proposicionais binários são tidos em conta somente alguns destes. Ao longo do século XX foram propostas várias notações que corrigem essa falência, dando lugar ao planejamento de interessantes problemas matemáticos. Objetivo: Neste artigo se apresenta a notação criada pelo norte-americano Charles Peirce, onde se mostram algumas das propriedades que tem está simbologia, e se evidenciam suas vantagens com respeito à tradicional. Método: Se descreve a notação proposta por Peirce, e se verificam algumas propriedades de carácter lógico geométrico e algébrico entre seus conectivos; também se analisa a possível atuação destas propriedades na notação usual. Resultados: Ademais de várias propriedades individuais e de múltiplas relações entre os conectivos, as simetrias do sistema completo dos conectivos proposicionais binários se evidenciam de maneira visual nos signos propostos por Peirce. Conclusão: Diversas bondades se percebem na notação proposta por Peirce, permitindo afirmar que a notação usual é superada de maneira clara pela simbologia desenhada pelo científico norte-americano.Palavras-chave: Charles S. Peirce, conectivo proposicional, operação, simetria, tabela de verdade.Antecedentes: En la notación tradicional para los conectivos proposicionales binarios son tenidos en cuenta solamente algunos de estos. A lo largo del siglo XX fueron propuestas varias notaciones que subsanan esa falencia, dando lugar al planteamiento de interesantes problemas matemáticos. Objetivo: En este escrito se presenta la notación creada por el norteamericano Charles Peirce, se muestran algunas propiedades de las cuales goza esta simbología, y se evidencian sus ventajas con respecto a la tradicional. Método: Se describe la notación propuesta por Peirce, y se verifican algunas propiedades de carácter lógico geométrico y algebraico entre sus conectivos; también se analiza la posible actuación de estas propiedades en la notación usual. Resultados: Además de varias propiedades individuales y de múltiples relaciones entre los conectivos, las simetrías del sistema completo de los conectivos proposicionales binarios se evidencian de manera visual en los signos propuestos por Peirce. Conclusión: Diversas bondades de las cuales goza la notación propuesta por Peirce, permiten afirmar que la notación usual es superada de manera clara por la simbología diseñada por el científico norteamericano
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Beneficios de la notación de Peirce para los conectivos proposicionales binarios
'Universidad Francisco de Paula Santander', 2016Co-Authors: Cardona Hurtado, Oscar AbelAbstract:Antecedentes: En la notación tradicional para los conectivos proposicionales binarios son tenidos en cuenta solamente algunos de estos. A lo largo del siglo XX fueron propuestas varias notaciones que subsanan esa falencia, dando lugar al planteamiento de interesantes problemas matemáticos. Objetivo: En este escrito se presenta la notación creada por el norteamericano Charles Peirce, se muestran algunas propiedades de las cuales goza esta simbología, y se evidencian sus ventajas con respecto a la tradicional. Método: Se describe la notación propuesta por Peirce, y se verifican algunas propiedades de carácter lógico geométrico y algebraico entre sus conectivos; también se analiza la posible actuación de estas propiedades en la notación usual. Resultados: Además de varias propiedades individuales y de múltiples relaciones entre los conectivos, las simetrías del sistema completo de los conectivos proposicionales binarios se evidencian de manera visual en los signos propuestos por Peirce. Conclusión: Diversas bondades de las cuales goza la notación propuesta por Peirce, permiten afirmar que la notación usual es superada de manera clara por la simbología diseñada por el científico norteamericano.Palabras clave: Conectivo proposicional, Charles S. Peirce, operación, simetría, tabla de verdad. AbstractBackground: In traditional Binary Notation for propositional connectives only some of these ones are taken into account. Throughout the twentieth century several Notations were proposed which overcome this flaw, leading to the proposal of interesting mathematical problems. Objective: This paper presents the Notation created by the American Charles Peirce, showing some of the properties of this symbols, and evidencing the advantages of these compared to the traditional. Method: the Notation proposed by Peirce is described, and some properties of the geometric and algebraic logical character among its connective are verified; also, the possible role of these properties in the traditional Notation is analyzed. Results: In addition to several individual properties and multiple relations between the connectives, the symmetries of the full set of Binary propositional connective is visually evident in the signs proposed by Peirce. Conclusion: Different benefits of the Notation proposed by Peirce, support the conclusion that the usual Notation is clearly surpassed by the symbolism designed by the American scientist.Keywords: Propositional connective, Charles S. Peirce, operation, symmetry, truth table. Resumo Antecedentes: Na notação tradicional para os conectivos proposicionais binários são tidos em conta somente alguns destes. Ao longo do século XX foram propostas várias notações que corrigem essa falência, dando lugar ao planejamento de interessantes problemas matemáticos. Objetivo: Neste artigo se apresenta a notação criada pelo norte-americano Charles Peirce, onde se mostram algumas das propriedades que tem está simbologia, e se evidenciam suas vantagens com respeito à tradicional. Método: Se descreve a notação proposta por Peirce, e se verificam algumas propriedades de carácter lógico geométrico e algébrico entre seus conectivos; também se analisa a possível atuação destas propriedades na notação usual. Resultados: Ademais de várias propriedades individuais e de múltiplas relações entre os conectivos, as simetrias do sistema completo dos conectivos proposicionais binários se evidenciam de maneira visual nos signos propostos por Peirce. Conclusão: Diversas bondades se percebem na notação proposta por Peirce, permitindo afirmar que a notação usual é superada de maneira clara pela simbologia desenhada pelo científico norte-americano.Palavras-chave: Charles S. Peirce, conectivo proposicional, operação, simetria, tabela de verdade
Oscar Abel Cardona-hurtado - One of the best experts on this subject based on the ideXlab platform.
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Beneficios de la notación de Peirce para los conectivos proposicionales binarios
Universidad Francisco de Paula Santander, 2016Co-Authors: Oscar Abel Cardona-hurtadoAbstract:Background: In traditional Binary Notation for propositional connectives only some of these ones are taken into account. Throughout the twentieth century several Notations were proposed which overcome this flaw, leading to the proposal of interesting mathematical problems. Objective: This paper presents the Notation created by the American Charles Peirce, showing some of the properties of this symbols, and evidencing the advantages of these compared to the traditional. Method: the Notation proposed by Peirce is described, and some properties of the geometric and algebraic logical character among its connective are verified; also, the possible role of these properties in the traditional Notation is analyzed. Results: In addition to several individual properties and multiple relations between the connectives, the symmetries of the full set of Binary propositional connective is visually evident in the signs proposed by Peirce. Conclusion: Different benefits of the Notation proposed by Peirce, support the conclusion that the usual Notation is clearly surpassed by the symbolism designed by the American scientist
в в шилов - One of the best experts on this subject based on the ideXlab platform.
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from the history of the Binary number system juan caramuel
Informatics in school, 2020Co-Authors: д м златопольский, в в шиловAbstract:The article, in addition to the previous publication of the authors, shows that the Binary number system was also described before the great German scientist Gottfried Wilhelm Leibniz, who did so in his work "Explication de l'Arithmetique Binaire" in 1703. In particular, the contribution of the Spanish polymath Juan Caramuel, who, in his book "Mathesis biceps vetus et nova" ("The two faces of mathematics — old and new"), published in 1670, considered Binary and other non-decimal number systems. In the book, he gave examples of the Binary Notation of numbers, compared the Binary and decimal number systems in terms of the number of digits in the Notation of numbers, etc. The scientist also suggested the possible use of the Binary system, in particular, in music.
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from the history of the Binary number system thomas harriot
Informatics in school, 2020Co-Authors: д м златопольский, в в шиловAbstract:For the first time in the Russian-language literature, the article analyzes the works of the English mathematician, geographer and astronomer Thomas Harriot (1560–1621) related to the Binary number system. The various variants of the Binary Notation of numbers presented in the works, examples of converting a decimal number to a Binary number and vice versa, examples of four arithmetic operations in the Binary number system, the execution methods of which coincide with modern ones, as well as an example of multiplication by an original method, the name of which can be translated in Latin as "another method is sequential addition" are given. All this allows us to conclude that Thomas Harriot described the Binary number system earlier than the great German scientist Gottfried Wilhelm Leibniz, who did so in his work "Explication de l'Arithmetique Binaire" in 1703.
д м златопольский - One of the best experts on this subject based on the ideXlab platform.
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from the history of the Binary number system juan caramuel
Informatics in school, 2020Co-Authors: д м златопольский, в в шиловAbstract:The article, in addition to the previous publication of the authors, shows that the Binary number system was also described before the great German scientist Gottfried Wilhelm Leibniz, who did so in his work "Explication de l'Arithmetique Binaire" in 1703. In particular, the contribution of the Spanish polymath Juan Caramuel, who, in his book "Mathesis biceps vetus et nova" ("The two faces of mathematics — old and new"), published in 1670, considered Binary and other non-decimal number systems. In the book, he gave examples of the Binary Notation of numbers, compared the Binary and decimal number systems in terms of the number of digits in the Notation of numbers, etc. The scientist also suggested the possible use of the Binary system, in particular, in music.
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from the history of the Binary number system thomas harriot
Informatics in school, 2020Co-Authors: д м златопольский, в в шиловAbstract:For the first time in the Russian-language literature, the article analyzes the works of the English mathematician, geographer and astronomer Thomas Harriot (1560–1621) related to the Binary number system. The various variants of the Binary Notation of numbers presented in the works, examples of converting a decimal number to a Binary number and vice versa, examples of four arithmetic operations in the Binary number system, the execution methods of which coincide with modern ones, as well as an example of multiplication by an original method, the name of which can be translated in Latin as "another method is sequential addition" are given. All this allows us to conclude that Thomas Harriot described the Binary number system earlier than the great German scientist Gottfried Wilhelm Leibniz, who did so in his work "Explication de l'Arithmetique Binaire" in 1703.
Eppstein David - One of the best experts on this subject based on the ideXlab platform.
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Making Change in 2048
LIPIcs - Leibniz International Proceedings in Informatics. 9th International Conference on Fun with Algorithms (FUN 2018), 2018Co-Authors: Eppstein DavidAbstract:The 2048 game involves tiles labeled with powers of two that can be merged to form bigger powers of two; variants of the same puzzle involve similar merges of other tile values. We analyze the maximum score achievable in these games by proving a min-max theorem equating this maximum score (in an abstract generalized variation of 2048 that allows all the moves of the original game) with the minimum value that causes a greedy change-making algorithm to use a given number of coins. A widely-followed strategy in 2048 maintains tiles that represent the move number in Binary Notation, and a similar strategy in the Fibonacci number variant of the game (987) maintains the Zeckendorf representation of the move number as a sum of the fewest possible Fibonacci numbers; our analysis shows that the ability to follow these strategies is intimately connected with the fact that greedy change-making is optimal for Binary and Fibonacci coinage. For variants of 2048 using tile values for which greedy change-making is suboptimal, it is the greedy strategy, not the optimal representation as sums of tile values, that controls the length of the game. In particular, the game will always terminate whenever the sequence of allowable tile values has arbitrarily large gaps between consecutive values
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Making Change in 2048
2018Co-Authors: Eppstein DavidAbstract:The 2048 game involves tiles labeled with powers of two that can be merged to form bigger powers of two; variants of the same puzzle involve similar merges of other tile values. We analyze the maximum score achievable in these games by proving a min-max theorem equating this maximum score (in an abstract generalized variation of 2048 that allows all the moves of the original game) with the minimum value that causes a greedy change-making algorithm to use a given number of coins. A widely-followed strategy in 2048 maintains tiles that represent the move number in Binary Notation, and a similar strategy in the Fibonacci number variant of the game (987) maintains the Zeckendorf representation of the move number as a sum of the fewest possible Fibonacci numbers; our analysis shows that the ability to follow these strategies is intimately connected with the fact that greedy change-making is optimal for Binary and Fibonacci coinage. For variants of 2048 using tile values for which greedy change-making is suboptimal, it is the greedy strategy, not the optimal representation as sums of tile values, that controls the length of the game. In particular, the game will always terminate whenever the sequence of allowable tile values has arbitrarily large gaps between consecutive values.Comment: 13 pages, 1 figure. To appear in the Proceedings of the 9th International Conference on Fun with Algorithms (FUN 2018), Leibniz International Proceedings in Informatic