On uncertain functions
In this paper, we analize some basic properties of the real functions f : R → R that satisfy the polynomial equation X 2 + 1 = 0 (that is, such that f2 + idR = 0, where f2 = f ◦ f). We prove their existence, give a characterization of such functions and show a concrete example from which infinite ot...
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| Formato: | Artículo revista |
| Lenguaje: | Español |
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Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación
2023
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| Acceso en línea: | https://revistas.unc.edu.ar/index.php/REM/article/view/41052 |
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I10-R366-article-410522023-08-08T16:31:14Z On uncertain functions Sobre funciones inciertas Freyre, Sebastián Sabia, Juan Funciones reales de una variable Continuidad Polinomios Espacios vectoriales Real univariate functions Continuity Polynomials Vector spaces In this paper, we analize some basic properties of the real functions f : R → R that satisfy the polynomial equation X 2 + 1 = 0 (that is, such that f2 + idR = 0, where f2 = f ◦ f). We prove their existence, give a characterization of such functions and show a concrete example from which infinite other examples can be derived. Next, we discuss some issues about their continuity. Finally, a classic linear algebra mechanism allows us to prove that, for every polynomial P ∈ Q[X], there exist functions f : R → R that satisfy the polynomial equation P = 0. En este trabajo, analizamos algunas propiedades básicas de las funciones reales f : R → R que satisfacen la ecuación polinomial X 2+1 = 0 (es decir, tales que f2+idR = 0, donde f2 = f ◦ f). Probamos su existencia, damos una caracterización de tales funciones y mostramos un ejemplo concreto del cual pueden derivarse infinitos ejemplos más. A continuación discutimos algunos aspectos sobre su continuidad. Finalmente, un mecanismo clásico del álgebra lineal nos permite probar que, para cualquier polinomio P ∈ Q[X], existen funciones f : R → R que satisfacen la ecuación polinomial P = 0. Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación 2023-04-27 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Artículo evaluado por pares application/pdf https://revistas.unc.edu.ar/index.php/REM/article/view/41052 10.33044/revem.41052 Revista de Educación Matemática; Vol. 38 Núm. 1 (2023); 10-21 1852-2890 0326-8780 spa https://revistas.unc.edu.ar/index.php/REM/article/view/41052/41145 https://creativecommons.org/licenses/by-sa/4.0/ |
| institution |
Universidad Nacional de Córdoba |
| institution_str |
I-10 |
| repository_str |
R-366 |
| container_title_str |
Revista de Educación Matemática |
| language |
Español |
| format |
Artículo revista |
| topic |
Funciones reales de una variable Continuidad Polinomios Espacios vectoriales Real univariate functions Continuity Polynomials Vector spaces |
| spellingShingle |
Funciones reales de una variable Continuidad Polinomios Espacios vectoriales Real univariate functions Continuity Polynomials Vector spaces Freyre, Sebastián Sabia, Juan On uncertain functions |
| topic_facet |
Funciones reales de una variable Continuidad Polinomios Espacios vectoriales Real univariate functions Continuity Polynomials Vector spaces |
| author |
Freyre, Sebastián Sabia, Juan |
| author_facet |
Freyre, Sebastián Sabia, Juan |
| author_sort |
Freyre, Sebastián |
| title |
On uncertain functions |
| title_short |
On uncertain functions |
| title_full |
On uncertain functions |
| title_fullStr |
On uncertain functions |
| title_full_unstemmed |
On uncertain functions |
| title_sort |
on uncertain functions |
| description |
In this paper, we analize some basic properties of the real functions f : R → R that satisfy the polynomial equation X 2 + 1 = 0 (that is, such that f2 + idR = 0, where f2 = f ◦ f). We prove their existence, give a characterization of such functions and show a concrete example from which infinite other examples can be derived. Next, we discuss some issues about their continuity. Finally, a classic linear algebra mechanism allows us to prove that, for every polynomial P ∈ Q[X], there exist functions f : R → R that satisfy the polynomial equation P = 0. |
| publisher |
Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación |
| publishDate |
2023 |
| url |
https://revistas.unc.edu.ar/index.php/REM/article/view/41052 |
| work_keys_str_mv |
AT freyresebastian onuncertainfunctions AT sabiajuan onuncertainfunctions AT freyresebastian sobrefuncionesinciertas AT sabiajuan sobrefuncionesinciertas |
| first_indexed |
2024-09-03T22:36:58Z |
| last_indexed |
2024-09-03T22:36:58Z |
| _version_ |
1809216195834937344 |