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On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.

16 votes
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356 views

Transcendence of sum of reciprocals of factorials

For $A \subseteq \mathbb{N}$, define $\displaystyle x_A = \sum_{n \in A} \frac{1}{n!}$. It is easy to see that for every infinite $A$, $x_A$ is irrational. Question: Is there an infinite $A \subseteq …
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