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Aug
29
comment Fractional part of $n\alpha$ is equidistributed
@GerryMyerson You probably meant the "trigonometric polynomials" are dense in the continuous functions.
Aug
27
comment Prove that $\det(I-CD)=\det(I-DC) $
The proof for non-invertible case falls short when the field is not infinite. But, the case can be taken care of by noting that the determinants are polynomials in the entries of matrices.
Aug
27
comment Prove that $\det(I-CD)=\det(I-DC) $
$AB$ and $BA$ has the same characteristic polynomial. This is well-known result.
Aug
27
comment On the number of group homomorphisms from $S_n$ to $S_m$
I think @soloveichik wants to say that there is an injective homomorphism maps $S_{m-1}$ to $S_m$. Thus, we cannot conclude that $n=m$ from $n\leq m$.
Aug
27
comment Commutative rings of order $p^3$.
See this: math.stackexchange.com/questions/368323/…
Aug
24
answered Proving the irrationality of the concatenation of the $n$th powers of primes
Aug
20
comment Primitive polynomials $P$ with $\gcd(P(x),P(y))=1$ for infinitely many $x,y$
Just Fermat's Little Theorem, $x^p -x \equiv x(x-1)\cdots (x-(p-1))$ mod ($p$).
Aug
19
comment $\lim_{n\to\infty} \frac{n}{a_n} = \lim_{x\to\infty} \frac{1}{x}\sharp \{n \leq x: n \in A\}$ when the limit exists.
Take care of $x$ in $a_n < x < a_{n+1}$.
Aug
19
answered Show $\forall \epsilon > 0$ there exists $\delta > 0$ such that $\int_E {|f|d\mu } < \varepsilon $ for all $E\in \cal M$ with $\mu(E) < \delta$
Aug
19
comment is my argument for $\lim_{n\rightarrow\infty}(a_n) = 0$ given $a_n = \tan(n) (\frac{1}{e})^{n}$ correct?
Great! We also have $\sum a_n$ converges.
Aug
18
comment Primitive polynomials $P$ with $\gcd(P(x),P(y))=1$ for infinitely many $x,y$
Great solution! By the way, (3) <=> (4) is clear without the VdM.
Aug
18
comment Find $\lim\limits_{n\to+\infty}\sqrt[n]{\prod\limits_{k=1}^{n}{n\choose k}}$
If you look at my answer, you will see that the limit should be $\infty$. So $\log L$ should be $\infty$ as well.
Aug
18
answered Find $\lim\limits_{n\to+\infty}\sqrt[n]{\prod\limits_{k=1}^{n}{n\choose k}}$
Aug
11
comment can i prove or reject it?
Any $\epsilon$ that is not $\pm 1$ can be used according to the assumptions of your problem.
Aug
10
comment Show that Var$(XY|Y) = Y^2$Var$(X|Y)$
You are right. This is essentially $Var(aX)= a^2 Var(X)$.
Aug
9
comment Show that $\mathbb{Q}(\sqrt{2},\sqrt{3},\dots,\sqrt{p},\dots)$ is an algebraic extension of $\mathbb{Q}$, for $p$ prime.
You need to prove that any number inside the field is algebraic.
Aug
9
comment Does $a_0=0, a_1=1, a_{n+2}=2a_{n+1}-3a_n$ ever return to 1 or -1 for $n>3$?
Great solution! By the way, the $\nu_2$ right after the downward arrow should be removed.
Aug
7
comment Proving that $\det(A) = 0$ when the columns are linearly dependent
The OP wants to break down the sum, so I thought OP was asking about multilinear property.
Aug
7
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Aug
7
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