Alexandre C.
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 Apr 2 comment How to confirm that if a function $f\circ f$ is a strong contraction, then $f$ has a fixed point or not? Hint: fixed points of $f\circ f$ are unique. Show that both $x_0$ and $f(x_0)$ are fixed points of $f\circ f$. Mar 28 comment How do I manipulate the sum of all natural numbers to make it converge to an arbitrary number? Riemann Theorem needs a series whose partial sums converge to begin with. Jun 21 comment How should one picture a topology/ topological space? Don't try to explicitly picture it -- "picturing" comes with habit. You should first learn the definition and memorize it, then you should gather enough different examples of topological spaces, and the next time you see a topological statement, try to instantiate it with the examples of topological spaces you know. After some time, topological statements will become second nature, like metric spaces are second nature to you. Jun 9 comment Is every right continuous local martingale of finite variation constant? A right continuous version of a compensated Poisson process provides an exemple of a right continuous FV martingale which is not constant. You need predictability of the difference to conclude that A = A'. Jan 18 comment $\lim_{{n}\to{\infty}} (n+1)!(e-1-{1\over2}-…-{1\over n!})= ?$ Is Cesaro-Stolz needed here ? The result is quite direct knowing that $a_n = \frac1{(n + 1)!}$ at leading order. Dec 21 awarded Constituent Dec 15 awarded Caucus Oct 8 awarded Nice Answer Oct 8 awarded Yearling Sep 24 awarded Autobiographer Aug 24 comment Limit of differences of truncated series and integrals give Euler-gamma, zeta and logs. Why? Note that you are looking at a particular case of Euler-Maclaurin formula: en.wikipedia.org/wiki/Euler%E2%80%93Maclaurin_formula Aug 5 awarded Teacher Aug 5 answered In calculus, which questions can the naive ask that the learned cannot answer? Aug 5 comment In calculus, which questions can the naive ask that the learned cannot answer? As a (negative) application, the Risch algorithm, which is supposed to decide whether a function admits a closed-form antiderivative (and computes it if it exsts), cannot decide in general exactly because of this. The proof of its termination relies on one being able to tell whether a given expression is zero. Aug 5 comment In calculus, which questions can the naive ask that the learned cannot answer? @MichaelHardy: Your operator is nothing more than the Euler-Maclaurin series :) Jan 25 awarded Supporter