Reputation
Next tag badge:
947/1000 score
267/200 answers
Badges
2 52 118
Newest
 Nice Answer
Impact
~1.5m people reached

20h
comment If a triangle has 2 sides of equal length, is it isosceles?
See this.
2d
comment If $\displaystyle\lim_{n\to\infty}|x_n|^{1/n} = L < 1$ then $\displaystyle\lim_{n\to\infty}|x_n|=0$.
Why wouldn't you use that (note though, it only holds for $n$ sufficiently large)?
2d
comment Characterization of the $L^p$ convergence.
See this for one approach.
Jul
30
comment Specific question on $l^p$ spaces and its dual in weak * topology
@A.G.It doesn't follow that a convergent subsequence exists; see this example. Perhaps I'm misunderstanding what you're saying... Martin, $B(l_\infty^*)$ is not weak* sequentially compact (nor is $B(X^*)$ if $X$ contains $\ell_\infty$ (or just $\ell_1(\Bbb R)$)). A proof of this can be found in Diestel's Sequences and Series in Banach Spaces.
Jul
29
comment Inserting parentheses to produce different values
Hmm... Is $(2\cdot3)^{(3}+4)$ legal? I would agree with you now.
Jul
29
comment Inserting parentheses to produce different values
I wonder what $6^7$ is,
Jul
29
answered Application of Baire Category theorem
Jul
29
comment Application of Baire Category theorem
A solution is contained in A Primer of Real Functions, Ralph P. Boas, Harald P. Boas on page 192. See here.
Jul
29
comment Discontinuities of an injective function from $\mathbb{R}$ to $\mathbb{R}$
$f(x)=x$, $x$ rational, $f(x)=x+1$, $x$ irrational.
Jul
28
comment A question about bijective functions
Onto is not needed.
Jul
28
comment What is the definition of a Critical Point?
As intimated above, "critical point" is not one of those "universally accepted" terms.
Jul
28
comment A question about bijective functions
I'd guess looking at $g(x)=f(x)+4-4x$ would be fruitful.
Jul
28
comment Generalized Fourier series in $L^2$ that do not converge pointwise a.e.
One might mention that in the linked paper, a specific permutation of the Haar basis, and a sketch of a proof that that it "works", is given.
Jul
28
comment How to find the antiderivative of f(x).
It's not so.${}$
Jul
28
comment Generalized Fourier series in $L^2$ that do not converge pointwise a.e.
Section 9 of the paper linked above gives an example of what you want, I think.
Jul
28
comment Generalized Fourier series in $L^2$ that do not converge pointwise a.e.
Of interest is Definition 8 and Theorem 11 from section 7 of this paper.
Jul
27
comment Cauchy Sequences--is the floor function of a Cauchy sequence also a Cauchy sequence?
What if you interspersed $1+1/n$ into your $a_n$?
Jul
27
comment Area under bijective decreasing function
Following Simon S's suggestion informally: The area under the graph of $f$ over $[2,4]$ is $\int_2^4 f(x)\,dx$. The area to the left of the graph of $f$ and to the right of $[3,5]$ on the $y$-axis is $\int_3^5 f^{-1}(x)\, dx$. The difference will leave you with two rectangles.
Jul
27
awarded  Nice Answer
Jul
27
answered Non strictly singular operators