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5h
comment Construction of a regular pentagon
@RoryDaulton It looks good, thanks!
5h
awarded  Nice Question
5h
comment Is a norm closed set(in the topology induced by the norm) weakly closed?
A bit simpler would be to take the set of standard unit vectors in $\ell_2$. This set is norm closed and has $0$ as a weak limit point.
9h
comment Proof that every point can lie on a tangent to a curve
Much cleaner than what I was going to do for the first part: Fix the vertical line $\ell$ through $x=a$. Show that the function $g$, where $g(x)$ is the $y$-coordinate of the intersection of $\ell$ with the tangent line to $p$ (of odd degree at least $3$) at $x$, is continuous. Use the convexity of $p$ to show $g$ takes arbitrarily "large" positive and negative values. Appeal to IVT to show every point on $\ell$ lies on a tangent line to $p$.
12h
comment how to prove that $\lim\limits_{n\to\infty} \left( 1-\frac{1}{n} \right)^n = \frac{1}{e}$
See this.
15h
comment The difference between a lemma and the Egorov's theorem
The set $F$ in the lemma depends on $\epsilon$ (and $\eta$ of course).
1d
comment Write $61.84 \times 10^{-3}$ in standard form
What is "standard form"?
1d
comment Is My Proof that $\pi^e < e^{\pi}$ Valid?
See this for other approaches.
1d
comment Is the product topology the most finest topology you can give to the cartesian product and why?
You could give it the discrete or indiscrete topology.
1d
comment measurable sets and open intervals
You can find, using regularity, an open set $O\supset A$ with $m(A\cap O)>r m(A^C\cap O)$. Write $O$ as a countable union of disjoint open intervals and show at least one of these intervals "works".
1d
answered Open set in a general metric space.
1d
comment Open set in a general metric space.
You can find a proof here (problem 7).
2d
comment Is it okay to perform the same row operation twice on opposite rows?
In the last step, you want to multiply the middle row by $2$ and add to the last (or multiply by $-2$ and subtract).
2d
comment set of all accumulation points of A is countable
Start with the set $A$ with elements $0,1/2,1/3,\ldots$. Then add points so that each element of $A$ becomes an accumulation point of $A$ in an appropriate manner.
2d
comment cross product of vector and direction
It's just a convention to have things well-defined. There may as well have been a "left hand rule".
2d
comment Journal related question.
Perhaps the folks at the Physics site would be more helpful.
2d
comment Constructing exponential function using a table of outputs
$g(x+1)/g(x)=$?
Jul
2
answered How to solve the integral $\int\tan^{3}x \sec^{3/2}x\; dx$?
Jul
2
comment How to solve the integral $\int\tan^{3}x \sec^{3/2}x\; dx$?
Your $du$ is wrong. $(\tan x)'=\sec^2 x$. Write the integrand as $\sec x \tan x \tan^2 x \sec^{1/2} x$ and let $u=\sec x$ ($du$ then is $\sec x\tan x$).
Jul
2
comment why separable normal space has only continuum many different open subsets?
See the first answer here.