user19038

 6h comment $\|f(x)-f(y)\|\geq ||x-y||$@Ian oh, what was I thinking... 6h comment $\|f(x)-f(y)\|\geq ||x-y||$Here is another useful link. 6h comment $\|f(x)-f(y)\|\geq ||x-y||$The argument in the first answer here should work. 15h comment $\# \mathbb{R}^2 \geq \# \mathbb{R}$?See this. 16h comment Why cantor function is not measurable?"Lebesgue measurable" means $(L,B)$- measurable. 1d comment Construction of a regular pentagon@RoryDaulton It looks good, thanks! 1d awarded Nice Question 1d 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. 1d comment Proof that every point can lie on a tangent to a curveMuch 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 $p$. 1d comment how to prove that $\lim\limits_{n\to\infty} \left( 1-\frac{1}{n} \right)^n = \frac{1}{e}$See this. 1d comment The difference between a lemma and the Egorov's theoremThe set $F$ in the lemma depends on $\epsilon$ (and $\eta$ of course). 1d awarded Supporter 2d comment Write $61.84 \times 10^{-3}$ in standard formWhat is "standard form"? 2d comment Is My Proof that $\pi^e < e^{\pi}$ Valid?See this for other approaches. 2d 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. 2d comment measurable sets and open intervalsYou 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". 2d answered Open set in a general metric space. 2d comment Open set in a general metric space.You can find a proof here (problem 7). Jul 3 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). Jul 3 comment set of all accumulation points of A is countableStart 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.