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" Hay un concepto que es el corruptor y el desatinador de los otros. No hablo del Mal cuyo limitado imperio es la ética; hablo del infinito. Yo anhelé compilar alguna vez su móvil historia. La numerosa Hidra (monstruo palustre que viene a ser una prefiguración o un emblema de las progresiones geométricas) daría conveniente horror a su pórtico; la coronarían las sórdidas pesadillas de Kafka y sus capítulos centrales no desconocerían las conjeturas de ese remoto cardenal alemán—Nicolás de Krebs, Nicolás de Cusa—que en la circunferencia vio un polígono de un número infinito de ángulos y dejó escrito que una línea infinita sería una recta, sería un triángulo, sería un círculo y sería una esfera (De docta ignorantia, I, 13). Cinco, siete años de aprendizaje metafísico, teológico, matemático me capacitarían (tal vez) para planear decorosamente ese libro. Inútil agregar que la vida me prohibe esa esperanza, y aún ese adverbio..."

Jorge Luis Borges en Avatares de la Tortuga.


2d
awarded  Quorum
Aug
23
reviewed Approve suggested edit on For which fields K is every subring of K…?
Jul
2
awarded  Curious
Jul
1
reviewed Approve suggested edit on Are Banach Manifolds intrinsically interesting?
Jun
29
revised Is the following sum irrational?
added 3 characters in body
Jun
29
reviewed Approve suggested edit on Combinatorics Problem: $\sum _{k=0}^{s-1} \binom{n}{k}=\sum _{k=1}^s 2^{k-1} \binom{n-k}{s-k}$
Jun
28
revised Primes from a Dirichlet sequence and an irrational number
added 110 characters in body
Jun
28
awarded  Nice Answer
Jun
28
revised Primes from a Dirichlet sequence and an irrational number
added 9 characters in body
Jun
28
comment Primes from a Dirichlet sequence and an irrational number
Apply reductio ad absurdum. Suppose that the number $\alpha$ is a rational number. We may even assume that $\alpha$ has a periodic decimal representation and that its period starts right after the decimal comma. Let $s$ denote the period length of $\alpha$. It is not difficult to establish, that for every $k\in \mathbb{N}$, the sequence $\{a_{i}\}_{i \in \mathbb{N}}$ has no more that $s$ terms of $k$ digits. Hence, $\sum_{i=1}^{\infty} \frac{1}{a_{i}} \leq \sum_{i=1}^{\infty} \frac{s}{10^{i-1}}$, which contradicts the divergence of the series $\sum_{i=1}^{\infty}\frac{1}{a_{i}}$...
Jun
28
revised Primes from a Dirichlet sequence and an irrational number
added 11 characters in body
Jun
28
revised Primes from a Dirichlet sequence and an irrational number
added 321 characters in body
Jun
28
answered Primes from a Dirichlet sequence and an irrational number
Jun
16
awarded  Deputy
Jun
16
reviewed Approve suggested edit on Are there any simple, interesting consequences to motivate the local Langlands correspondence?
Jun
15
reviewed Edit suggested edit on Understanding lie bracket of simple Lie algebra $W(2)$
Jun
15
revised Understanding lie bracket of simple Lie algebra $W(2)$
Minor English corrections, and added MathJax
Jun
15
reviewed Edit suggested edit on Number of zeros of a polynomial in the unit disk
Jun
15
revised Number of zeros of a polynomial in the unit disk
Change the size of the brackets
Jun
15
reviewed Approve suggested edit on Enumeration of a finite group