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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