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2h
answered Countable set in a Banach space which spans densely?
18h
comment Find $f$ so that $\int_{1}^{\infty}f(x)dx$ exists, but $\displaystyle \lim_{x\to\infty}f(x)$ does not exist?
$f(x)=1$ if $x$ is an integer, $f(x)=0$ otherwise. (More interesting examples can be obtained by taking "spikes" at the integers whose areas tend to $0$ sufficiently fast.)
19h
comment Continuous and bounded - Check my proof please
First find $M>0$ with $|f(x)|<1$ for $x\ge M$. Then find a bound for $|f|$ on $[0, M]$. One step to go after that ...
19h
comment An exercise about Lebesgue measure
Should be $A_k$ above...
19h
comment An exercise about Lebesgue measure
Write $B=\bigcap\limits_{n=1}^\infty \bigcup\limits_{k=n}^\infty A_n$.
22h
comment Where can I find a good drawing software?
TeX and Tikz/pgf.
23h
comment What does “2- place real function” mean?
I'd guess, it's a function of two variables. e.g. $f:\Bbb R^2\rightarrow\Bbb R$.
23h
comment Pointwise convergence - $\frac{nx}{1+n \sin(x)}$ , $x \in [0, \frac{\pi}{2}]$
It converges to $f(x)=\cases{{x\over\sin x},& $0<x\le\pi/2$\cr 0, & $x=0$ }$.
23h
comment Pointwise convergence - $\frac{nx}{1+n \sin(x)}$ , $x \in [0, \frac{\pi}{2}]$
$f_n(0)= 0/(1+0)=0$ for each $n$.
1d
comment Why does $\int_0^{\infty}e^{-\frac{z^2}{4}}dz=\sqrt{\pi}\ $?
Substitute $u=x/2$.
1d
comment Determining whether a set is linearly independent.
The book is in error...
1d
comment How do I calculate $ \int_{-\infty}^{\infty} e^{-ax^2} \;\mathrm{d}x$ for $a>0 $
You may find this helpful also.
1d
comment How do I calculate $ \int_{-\infty}^{\infty} e^{-ax^2} \;\mathrm{d}x$ for $a>0 $
See this.
1d
comment Show that if $X$ is sequentially compact, then $X$ is complete and totally bounded
Proving that sequential compactness implies compactness is a bit harder than proving the OP's statement (and in fact, many proofs that sequential compactness implies compactness use the OP's statement).
2d
comment Exceptions in functions
Equations aren't called "even"; instead, one would say the graph is symmetric with respect to the $y$-axis. The graph of $x^2+y^2=1$ indeed has this property (it's the unit circle).
May
21
comment Open-Set Correspondence $\implies$ Continuity
It looks ok. You should mention your $n$-ball of radius $\delta$ has center $a$. This $n$-ball is the red disc. Your (otherwise nice) picture is mislabelled. The red disc is $B^{-1}$?)
May
21
answered Normed space where unit ball's weak and norm topology coincide?
May
21
comment Normed space where unit ball's weak and norm topology coincide?
This is of interest.
May
21
comment The function is not continuous
What is $g$? Perhaps this is what you're after.
May
21
comment Which of the following sets have the cardinality the same as $R$
For $Y$, a continuous function is determined by its values on the rationals.