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Feb
20
comment Suppose $f:\mathbb{R} \to \mathbb{R}$ is such that $f(x) \leq 0$ and $f''(x) \geq 0, \forall x.$ Prove $f$ is constant.
Proof idea: $f$ is convex so it lies above its tangents. Their slopes can't be non-zero or else $f$ would have a $+\infty$ limit at $-\infty$ or $+\infty$.
Feb
17
answered Evaluate $P(A^C\cup \!\,B^C)$
Jan
8
revised Finding radius of convergence for taylor series of $\frac{z}{e^z-1}$
added 23 characters in body
Jan
8
comment Finding radius of convergence for taylor series of $\frac{z}{e^z-1}$
Good remark! I'll modify my answer.
Jan
7
comment Finding radius of convergence for taylor series of $\frac{z}{e^z-1}$
Can you solve the equation $e^z-1=0$?
Jan
7
answered Finding radius of convergence for taylor series of $\frac{z}{e^z-1}$
Jan
7
comment Finding radius of convergence for taylor series of $\frac{z}{e^z-1}$
$0$ is clearly a false singularity of this meromorphic function on $\mathbb{C}$. It can obviously be extended as an holomorphic function on a neighborhood of $0$ by setting $f(0)=1$.
Dec
9
awarded  Caucus
Oct
7
revised Proof the bijectivity of the exponential function mod $2 \pi i$
Incorrect tag. Improved LaTeX.
Oct
7
suggested approved edit on Proof the bijectivity of the exponential function mod $2 \pi i$
Sep
30
awarded  Explainer
Sep
18
comment Prove $\sin(x)< x$ when $x>0$ using LMVT
Or you can juste choose $x$ in $(0,+\infty)$ from the beginning.
Sep
8
awarded  Yearling
Sep
4
revised How to prove property of complex powers
Improved LaTeX, changed tag
Sep
4
suggested approved edit on How to prove property of complex powers
Aug
28
awarded  Announcer
Aug
2
comment Video lectures of algebraic geometry (Hartshorne, Shafarevich, … )
Harpreet Bedi has nice videos here.
Jul
4
revised If $Du=0$ a.e. , does $u=c$ a.e.?
Added LaTeX, improved the message.
Jul
4
suggested approved edit on If $Du=0$ a.e. , does $u=c$ a.e.?
Jun
10
comment Show that $|z+1|\le|z+1|^2 +|z|$ for all $z \in \mathbb{C}$
I think it's badly written : "If $1\leqslant |z+1|$, then $|z+1|\leqslant|z+1|^2$ hence $|z+1|\leqslant |z+1|^2+|z|$, now I must show that the inequality is also true when $|z+1|<1$, but this is where I'm stuck."