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seen Jan 22 at 17:32

Math and stuff.


Jan
22
comment How to find all integer solutions of $p^2+q^2=((2q+1)^2+q+1)^2+1$
For $|q|\le 10^7$ there are no further solutions (Python checked it for me).
Jan
22
comment How to find all integer solutions of $p^2+q^2=((2q+1)^2+q+1)^2+1$
$(1,-1)$ is also a solution.
Jan
22
answered $e^{x} > 1$ and $0 < e^{x} < 1$
Jan
22
comment How can I prove this integration result?
Use the functional equation of the beta function. It is almost the Wallis integral.
Jan
22
answered question 3.40 from Folland Real Anyalysis
Dec
10
awarded  Caucus
Oct
30
revised Convergence of the sequence $\frac{1}{n\sin(n)}$
deleted 695 characters in body
Oct
30
comment Show that the measure is Lebesque
For instance, take the decimal expansion of your irrational number and truncate it after the $n$th digit behind the decimal point (that is, set all the digits after the $n$th to $0$). The resulting numbers are a rational approximation of your chosen irrational.
Oct
24
comment $\lim _{x\to 2}\:\frac{x}{x^2-4}$ Why using L'hopital rule is wrong?
It's not a limit of the indeterminate form $0/0$.
Oct
24
revised How to determine volume of parallelepiped by 4 points
deleted 27 characters in body
Oct
24
answered How to determine volume of parallelepiped by 4 points
Oct
24
answered Why $L^1$ is not reflexive
Oct
23
answered Proving that $(A^t)^t=A$
Oct
23
comment Show that the measure is Lebesque
What you did until now is only enough for $\mu([a,b))=b-a$ if $b-a\in\mathbb{Q}$. For irrational $b-a$ approximate by rationals and use regularity. Then it follows that $\mu$ is the Lebesgue measure.
Oct
21
comment Show that the measure is Lebesque
No, then its ok.
Oct
21
comment Tonelli-Fubini Theorem for two copies of $\mathbb{N}$ with counting measure
Then it's about interchanging sum and integral.
Oct
20
comment Show that the measure is Lebesque
Ok, but you are implicitly assuming $b-a=m/n$, $m,n\in\mathbb{N}$.
Oct
20
comment Show that the measure is Lebesque
It's not written down correctly, but you are on the right track. Be careful with $\cdots$.
Oct
20
comment Tonelli-Fubini Theorem for two copies of $\mathbb{N}$ with counting measure
It says that you can interchange the sum signs in $\sum_n \sum_m a_{n,m}$ if $a_{n,m}\ge 0$ or $\sum_{n,m} |a_{n,m}|<\infty$.
Oct
20
comment Show that the measure is Lebesque
I think I said enough. Translation invariance, additivity, .. play around. You will see. If you really can't solve it, look it up somewhere, this is a standard problem.