No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. - David Hilbert Citado en E Maor, Al infinito y más allá (Boston, 1987).

Carolina Lega (CAR), Juliana Quintero (JUL), Andrés Forero (AND) y Juan Gabriel Malagón (GAB).
Conferencia dada el Jueves 19 de octubre, 2000 en la Universidad de los Andes.

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Orden de la exposición:

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Conceptos relacionados:

- Paradoja: A statement which appears self-contradictory or contrary to expectations, also known as an antinomy. Curry (1977, p. 5) uses the term pseudoparadox to describe an apparent paradox for which, however, there is no underlying actual contradiction. Bertrand Russell classified known logical paradoxes into seven categories. (tomado de http://mathworld.wolfram.com/).
- Teoría de tipos
- Axioma de abstracción

Teoría de conjuntos:
  - Ordinal
  - Cardinal
  - Aleph 0
  - Ómega
  - Números transfinitos
  - Infinito potencial

- Lógica simbólica
- Sistema axiomático
- Axiomas de Peano
- Teoremas
- Inconsistencia de un sistema formal
- Incompletitud de un sistema formal

- Formalismo
- Platonismo
- Intuicionismo

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Curiosidades / Paradojas:

Paradoja de Cantor: The set of all sets is its own power set. Therefore, the cardinality of the set of all sets must be bigger than itself.

Paradoja de Sócrates: Sólo sé que nada sé.

Smarandache Paradox: Let A be some attribute (e.g., possible, present, perfect, etc.). If all is A, then the non-A must also be A. For example, "All is possible, the impossible too," and "Nothing is perfect, not even the perfect."

Liar's Paradox: The paradox of a man who states "I am lying." If he is lying, then he is telling the truth, and vice versa. Another version of this paradox is the Epimenides paradox. Such paradoxes are often analyzed be creating so-called "metalanguages" to separate statements into different levels on which truth and falsity can be assessed independently. For example, Bertrand Russell noted that, "The man who says, `I am telling a lie of order n' is telling a lie, but a lie of order " (Gardner 1984, p. 222).

Berry Paradox There are several versions of the Berry paradox, the original version of which was published by Bertrand Russell and attributed to Oxford University librarian Mr. G. Berry. In one form, the paradox notes that the number "one million, one hundred thousand, one hundred and twenty one" can be named by the description: "the first number not nameable in under ten words." However, this latter expression has only nine words, so the number can be named in under ten words, so there is an inconsistency in naming it in this manner!

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Matemáticos relacionados con el tema:

- Georg Cantor (1845 - 1918)
- Cesare Burali Forti (1861 - 1931)
- Bertrand Russell (1872 - 1970)
- David Hilbert (1862 - 1943)
- Kurt Gödel (1906 - 1978)

- Giuseppe Peano (1858 - 1932)
- Luitzen Egbertus Jan Brouwer (1881- 1966)
- Ernst Friedrich Ferdinand Zermelo (1871 - 1953)
- Friedrich Ludwig Gottlob Frege (1848 - 1925)
- Alfred North Whitehead (1861 - 1947)

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Texto escrito

Por el momento no tenemos nada...

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Cosas por definir

- Título de la exposición.
- Cómo participará el público.
- Conclusiones de la exposición.
- Duración de los subtemas.
- Recursos pedagógicos (carteleras, computador, colombinas, papeles, etc...).
- Trancisiones de un tema al otro (quién, cómo).

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Bibliografía:

Beginnings of Set Theory
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Beginnings_of_set_theory.html

G.J. CHAITIN, A Century of Controvesy over the Foundations of Mathematics.
http://www.umcs.maine.edu/~chaitin/lowell.html

Gödel's Incompleteness Theorem
http://www.miskatonic.org/godel.html

AROUND GOEDEL'S THEOREM
http://www.ltn.lv/~podnieks/index.html

Russell's Paradox
http://plato.stanford.edu/entries/russell-paradox/

Paias (inconsistency of set theory)
http://www.paias.com

Philosophies of Mathematics
http://students.washington.edu/zippy/ee/ee-ruth_alderson.html

Relevance of the Axiom of Chice
http://www.cs.unb.ca/profs/alopez-o/math-faq/node69.html

Fun with Paradox
http://www.math.niu.edu/~rusin/known-math/97/paradox

Infinite Ink's MAthematics Pages
http://www.ii.com/math/

Peter Suber, "Infinite Sets"
http://www.earlham.edu/~peters/writing/infapp.htm

Infinity and the Limits of Thought
http://www.math.tamu.edu/~Aysu.Bilgin/inf.html

Set Theory and Foundations
http://www.seanet.com/~ksbrown/ifoundat.htm

XX Century Paradoxes
http://www.dm.uniba.it/psiche/bas3/node4.html

NORTHROP, Eugene P. Paradojas matemáticas.

CAR, JUL y GAB: Mándenme por email la bibliografía de los textos (AUTOR, Título, año, ciudad, edición, #pags), o de las páginas de Internet que hayan consultado.

En esta página he compilado la bibliografía de Internet

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última modificación: martes 10 de octubre de 2000.