13,340 reputation
22788
bio website lama.univ-savoie.fr/~bogosel
location Chambery, France
age 26
visits member for 3 years, 11 months
seen 4 hours ago

Third year Phd student at Universite de Savoie, France. Interests: free boundary problems, PDE, spectral optimization, numerical analysis.


Jan
3
comment Cantor's infinities, and the cardinality of reals vs. complex
It has been proved that it is not possible to prove or disprove that $\aleph_1=2^{\aleph_0}$?
Dec
30
comment Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?
Very nice answer.
Dec
30
comment Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?
@AndresCaicedo: Yes, of course, but it is possible to prove that this function has the Darboux property without passing through the theorem about the derivative; using only the definition.
Dec
30
comment Continuity $\Rightarrow$ Intermediate Value Property. Why is the opposite not true?
Maybe you should have added some details on the part "clearly satisfies the intermediate property" to convince the OP that this example is simpler than the derivative one.
Dec
28
comment A problem with 26 distinct positive integers
@SteveKass: Got it fixed
Dec
27
comment Construct triangle given inradius and circumradius
I think I've also found a visual counterexample.
Dec
27
comment Prove that $\,f=0$ almost everywhere.
Use monotone convergence theorem: en.wikipedia.org/wiki/Monotone_convergence_theorem
Dec
27
comment Prove that $\,f=0$ almost everywhere.
@YiorgosS.Smyrlis: Even better for the last step: each Lebesgue measurable set can be approximated from above with open sets and open sets are countable union of intervals.
Dec
27
comment Prove that $\,f=0$ almost everywhere.
@YiorgosS.Smyrlis: $f$ is integrable by definition. The fact that $\int_I f=0$ comes from $\int_0^x f=0$. Every Borel set can be obtain by a countable number of unions/intersections.
Dec
27
comment What does it mean that a function continuous in an environment $M_0(x_0,y_0)$?
You may find Google helpful: en.wikipedia.org/wiki/Neighbourhood_(mathematics) more details here.
Dec
27
comment What does it mean that a function continuous in an environment $M_0(x_0,y_0)$?
Come on... :) A ball of center $x_0$ and radius $r$ is the set of points $x$ which are at a distance smaller than $r$ from $x_0$. Just imagine a 3D ball.
Dec
27
comment Prove that $\,f=0$ almost everywhere.
@Roozbeh-unity: Take absolute values before dividing with $(x-y)$.
Dec
27
comment Prove that $\,f=0$ almost everywhere.
@Roozbeh-unity: I thought of that, but I think a direct solution seems more appropriate here. I think the proof of the theorem you mention is not simpler than what I did here.
Dec
26
comment How many times is the digit $3$ repeated in $9^{666}$?
As the tags suggest, it might be an olympiad problem, and I surely would like to see a solution which does not include computer programs. I don't think this question needs more context than the famous batman question...
Dec
26
comment Diophantine equation: $x^2+y^2+z^2=n(xy+yz+zx)$
It is possible to prove that $x^2+y^2=nxy$ has solutions only if $n=2$. If it has solutions, pick the one with $|x|+|y|$ minimal. Then if there exists $p$ prime which divides $x$ it follows immediately that $p$ divides $y$ so we can factor out a $p^2$ and obtain a solution with smaller $|x|+|y|$. Therefore there does not exist $p$ prime which divides $x$ or $y$ and so $x=y=1$ and $n=2$.
Dec
26
comment Diophantine equation: $x^2+y^2+z^2=n(xy+yz+zx)$
if $z=0$ then you are left with $x^2+y^2=nxy$ which has solutions for $n=2$.
Dec
25
comment How many times is the digit $3$ repeated in $9^{666}$?
The answer seems to be 60. (done with pari-gp)
Dec
25
comment Proving continuity at a point $x_0$.
If you have a sequence in $A\cup B$ then there are a few cases: 1. All terms from a point on are in $A$. 2. All terms from a point on are in $B$. 3. There are two other sequences, one in $A$ and one in $B$ such that their union is the initial sequence.
Dec
25
comment Calculation of $\lambda$, If $x^2+2(a+b+c)\cdot x+3\lambda \cdot (ab+bc+ca) = 0$ has real roots
It seems that you wrote the inequalities backwards... The equilateral triangle doesnt verify that.
Dec
21
comment Proving that a polynomial $|P(x)|=e^x$ has a solution
@GinKin: The polynomial is a constant in the first case.