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8m
comment fn converges to f pointwise where all functions fn are bounded and f is unbounded: Is this example correct?
Yes, it is correct.
20m
comment How to show that there exists a sequence in $[0,1]$ such that the set of accumulation points of the sequence is $[0,1]$
Then if $r$ is in $[0,1]$, for any integer $n$, $r\in [k/2^n, (k+1)/2^n]$ for some $k$ and the endpoints of these intervals are members of your sequence.
22m
comment How to show that there exists a sequence in $[0,1]$ such that the set of accumulation points of the sequence is $[0,1]$
I mean, go down to $3/4$, then $2/4$ (was skipped), then $1/4$, ...
36m
comment How to show that there exists a sequence in $[0,1]$ such that the set of accumulation points of the sequence is $[0,1]$
It would be easier if you didn't skip terms ...
2h
comment mathematical calculation problems
Hmm. The sum of three odd numbers is always ...
2h
comment What is the outer measure of the union of uncountably many sets of measure 0.
Singleton sets have measure zero. Every set is a union of singletons.
2h
comment Advanced (for me) algebra and mean
The sum of the $n$ peoples' IQ is $n\cdot 111$. Write the mean for the $n+1$ people in terms of $n$. You know this is $110$. Solve the equation for $n$.
7h
comment How do I show that $0<a_n^2<a_n$ If $\sum _{n=1}^\infty a_n$ is convergent?
Eventually, $a_n<1$ and then $a_n^2<a_n$.
8h
comment Convergence of series
Use $ab\le{1\over2}(a^2+b^2)$ and the Comparison Test.
1d
comment Does Tom catch Jerry?
Tom never catches Jerry, from what I recall.
Apr
21
comment Does every closed subspace of a dual space correspond to a closed subspace of its predual?
I may be missing something here, but, for example, $c_0$ is a closed subspace of $\ell_\infty$ that is not a dual space (that is, $c_0$ has no predual).
Apr
20
comment Integral of ln (3x) / x
Yes, it is.${}$
Apr
19
awarded  Good Answer
Apr
17
comment if a sequence converges in measure in $L^p$, then converging for weak topology.
First, use this. Then show (by contradiction, e.g.) that convergence in measure suffices.
Apr
17
comment Can I find $\sum_{k=1}^n\frac{1}{k(k+1)}$ without using telescoping series method?
Be sure to put on your hair shirt first :)
Apr
17
comment For which values of the parameter $p$ the following series is convergent?
To evaluate $\int{1\over x(\ln x)^p}\,dx$, substitute $u=\ln x$.
Apr
17
comment sequence in $L^1$ converging pointwise a.e., but not weakly.
Look at $f_n=n\chi_{[0,1/n]}$.
Apr
17
comment For which values of the parameter $p$ the following series is convergent?
You could use the Integral Test.
Apr
17
comment sequence in $L^1$ converging pointwise a.e., but not weakly.
Yes. Norm convergence implies weak convergence in any normed space.
Apr
11
comment How could this be true $n=\log(e^n)$?
$\log_a x=y\iff a^y=x$.