## jueves, 18 de noviembre de 2010

### En la opinión de Zeilberger

«... In my ultrafinitist weltanschauung, the great significance of both Gödel's famous undecidability meta-theorem, and Paul Cohen's independence proof is historical (or as Cohen would put it, "sociological"). Both are reductio proofs that anything to do with infinity is a priori utter nonsense, debunking the age-old erroneous belief of human-kind in the actual (and even potential) infinity. Granted, many statements: like "m+n=n+m for all (i.e. "infinitely" many) integers m and n" could be made a posteriori sensible, by replacing the phrase "for all" (when it ranges over "infinite" sets) by the phrase for "symbolic (commuting) variables (or rather letters) m and n". We have to kick the misleading word "undecidable" from the mathematical lingo, since it tacitly assumes that infinity is real. We should rather replace it by the phrase "not even wrong" (in other words utter nonsense), that cannot even be resurrected by talking about symbolic variables. Likewise, Cohen's celebrated meta-theorem that the continuum hypothesis is "independent" of ZFC is a great proof that none of Cantor's א-s make any (ontological) sense.»

## sábado, 6 de noviembre de 2010

### 15 de Brumario

La pregunta del momento: Sea (X,τ) un espacio topológico y D un subconjunto denso de X. ¿Será cierto que si por cada d ∈ D elegimos un abierto (propio) Ad tal que dAd, entonces

$\mathbf{X} = \bigcup_{\mathbf{d} \in \mathrm{D}} \mathbf{A}_\mathbf{d}$ ?

Por favor, no dejen de intentarle...