How can we show that the function $n \mapsto e_n$, where $e_n$ is the $n$-th digit in the decimal expansion of $e$, is computable?
I have some idea in terms of Cantor's diag. argument, but I need to think along the lines of writing a series expansion, and Church's thesis.
Can someone produce the series as discussed below? thanks
Hint: because $e$ is not a rational number, for each rational number $r$ you can produce a sufficiently good approximation to $e$ to tell whether $e$ is greater than $r$ or less than $r$. The way to make the approximation is to use a series for $e$ for which you can estimate the error for each partial sum.