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bio website math.ntnu.no/~hanche
location Trondheim, Norway
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visits member for 2 years, 10 months
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Nov
3
comment Prove that $(f \circ g)^{(n)}$ exists for any n
Wording can be quite important in mathematics: When you say “prove that … for any value of $n$” you are asking for a proof of a statement of the form “for all $n$, …”. But that makes no sense here, since $n$ is implicitly already given a fixed (but unknown) value in the first sentence, so it is no longer free to vary. If the second sentence went “prove that … no matter what the value of $n$ is”, it would be better, since you are not really invoking the dreaded ∀ quantifier.
Nov
3
comment Diagonalizable Matrix over the complex field
If $A^2=A$ and $A$ is invertible, then it is that easy. However, $A$ may not be invertible. But here is a hint: What are the possible eigenvalues of $A$? Also, what happens if you square $I-A$?
Nov
3
comment Using Fatou's lemma
For which $x$ is $\inf_{n\ge m}\chi_{E_n}(x)=1$? For which $x$ is it zero? (Do you see why it has no other values than those two?) Express your answers in terms like “for all $n\ge m$ …” or “for some $n\ge m$ …”, then interpret that as unions or intersections.
Nov
2
answered Using Fatou's lemma
Oct
31
comment Simplify the product of two sums
There isn't a lot you can do, since arithmetic series are easily summed, while there is no simple expression for Harmonic numbers.
Oct
31
comment Alternative proof of "Every linear mapping on a finite dimensional space is continuous”
I haven't looked at the detail, but this should work the way you outlined it. There is a big but though: It relies on the equivalence of norms on finite dimensional spaces. That is the hard bit, and your proof does nothing to change that
Oct
28
comment Multiplication in the Galois field GF(3^3)
@Thomas: Nah, I'll just upvote the who did instead. It's far easier. There, done.
Oct
28
comment Multiplication in the Galois field GF(3^3)
it's not as simple as a wrong sign, is it? $x^3=f(x)-(2x^2+1)$ …
Oct
26
comment Find the value of x
Did you try rewriting the factors along the lines of $1-1/n^2=(n^2-1)/n^2=(n-1)(n+1)/n^2$? It looks to me like you could get some cancellation going …
Oct
26
reviewed Approve suggested edit on Find the value of x
Oct
26
comment Supremum of a sequence of measures again a measure?
What have you tried? To get you started, if $\nu$ is this set function, what would it take for it to satisfy $\nu(A\cup B)=\nu(A)+\nu(B)$ for disjoint $A$ and $B$? You could play with a measurable space of just two points.
Oct
25
comment The isomorphisms between $S^5$ and $SU(3)/SU(2)$?
I can't claim any expertise on this, and it may have been decades since last I looked at such things, but $SU(3)$ acts on the unit sphere in $\mathbb{C}^3$ (i.e., on $S^5$), and a copy of $SU(2)$ would be the stabilizer of $(0,0,1)$, say. From these facts, you should be able to piece together an isomorphism.
Oct
24
comment Integrating (floor(x) e^-x) from 0 to inf
What have you tried? Notice that floor(x) is piecewise constant.
Oct
24
comment Lebesgue Measure: No Atoms!
@Freeze_S If $r<s$ then $B_r\cap A\le B_s\cap A$, so $|\lambda(B_s\cap A)-\lambda(B_r\cap A)|=\lambda((B_s\cap A)\setminus(B_r\cap A))=\cdots$ $\cdots=\lambda((B_s\setminus B_r)\cap A)\le\lambda(B_s\setminus B_r)=\lambda(B_s)-\lambda(B_r)=(2s)^n-(2r)^n$.
Oct
23
answered Gamma function in $C^{2}$
Oct
23
comment Gamma function in $C^{2}$
Indeed, but the question is tagged with measure-theory, so we (or rather the OP) will probably have to assume a different toolkit.
Oct
23
comment Gamma function in $C^{2}$
You should go for $C^1$ first. Try to write up the definition of the derivative, and see if you can move the limit operation inside the integral. Or did you try that already?
Oct
23
comment Lebesgue Measure: No Atoms!
I added an explanation.
Oct
23
revised Lebesgue Measure: No Atoms!
Add some detail
Oct
23
comment Lebesgue Measure: No Atoms!
My answer could be a different way.