4h
comment Cantor Set contain a nonmeasuable set.
Subsets of a Lebesgue measurable set of measure zero are measurable (and have measure zero).
Mar
29
comment Real Analysis Exercise
Show it's a subspace. Then show it contains a set whose linear span is dense (like the set of standard unit vectors). Complete sets are closed.
Mar
28
comment Does $\int_{0}^{1} |f(t)|dt=0$ imply that $f(t)=0\ \text{for all } t \in [0,1]$?
$f$ could be non-zero at a single point (or more).
Mar
27
awarded Yearling
Mar
27
awarded Yearling
Mar
26
comment Proof of small part of Euclid's proof of pythagorean theorem
For the shaded triangle on the left, find the area using the bottom of the small square as the base.
Mar
25
comment differentiate the xth root of x
Set $q=x$ and $s=1/x$. Apply the multivariable chain rule to $z=q^s$: ${dz\over dx}={\partial z\over\partial q}\cdot{dq\over dx}+{\partial z\over\partial s}\cdot{ds\over dx}$.
Mar
24
revised what is the answer about this function?
edited tags
Mar
21
revised How to create a page with a structure like this?
deleted 29 characters in body
Mar
21
revised How to create a page with a structure like this?
added 104 characters in body
Mar
21
answered How to create a page with a structure like this?
Mar
21
comment Proving set is dense
Given $x\in B$ and $\epsilon>0$, choose $n$ with $x/n<1$. Then choose $y\in A$, with $|y-x/n|<\epsilon/n$.
Mar
20
comment Are the real numbers dense in the comlex numbers?
Is a line dense in a plane?
Mar
14
comment What this notation R^3 ∖ (0, 0, 0) means?
"i.e."="that is". He tells you what it means.
Mar
14
comment proof of a calculus fact
Fix $p$ and calculate $\lim\limits_{b\rightarrow\infty}\int_a^b 1/x^p\,dx$.
Mar
14
comment Find all $ p \ge 1 $ for which the Hölder norm $\|\cdot\|_p $ is generated by a scalar product.
They don't satisfy the equality for $p=1$ (the LHS is then $8$ and the RHS is $4$). The equality is not satisfied for these vectors for any $p\ne2$; this shows the norm is not induced from an inner product for $p\ne2$.
Mar
14
comment Find all $ p \ge 1 $ for which the Hölder norm $\|\cdot\|_p $ is generated by a scalar product.
Just compute with $x=(1,0,0,\ldots)$ and $y=(0,1,0,0,\ldots)$.
Mar
13
comment Sine of a truncated value of $\pi$
What is $\sin\pi$?
Mar
11
awarded metric-spaces
Mar
10
comment Find where this series uniformly converges
Note, though, that $s_k(0)=0$ for all $k$.
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