108,650 reputation
698199
bio website von-eitzen.de/math/tntrep.xml
location Bonn, Germany
age 48
visits member for 1 year, 11 months
seen 12 mins ago

I did study math and had a knack for it, but I am sooo out of that business now ...


Oct
12
comment Question on dense sets
You need a lot more than density. Even if $\overline Y=\overline{Y^c}=X$, there are counterexamples: Let $X=\mathbb R$, $Y=\mathbb R\setminus\mathbb Q$, $f(x)=0$, $g(\frac nm)=\frac1m$ for $\frac nm\in\mathbb Q$ and $=0$ otherwise.
Oct
12
reviewed Leave Open Question on dense sets
Oct
12
comment If $b-c>1/2, b_n\to b$ and $c_n\to c$, there is $n$ such that $b_n,c_n \in (c-1/4,b+1/4)$ for all $n > N$
Indeed, $b-c>-\frac14$ is sufficient.
Oct
12
answered Does the 13th sphere fit in?
Oct
12
answered The limit as $x \to \infty$ of $ \frac {\sqrt{x+ \sqrt{ x+\sqrt x}} }{\sqrt{x+1}}$
Oct
12
revised Finding all finite field embeddings
deleted 53 characters in body
Oct
12
comment Finding all finite field embeddings
What is the difference between $GF((2^2)^2)$ and $GF(2^4)$ in the first place? Both are simply $GF(16)$.
Oct
12
answered Finding all finite field embeddings
Oct
12
comment Proving that $n!≤((n+1)/2)^n$ by induction
Actually, to properly remove the "$\ldots$" in your proof one does need induction (or: if you use the recursive definition of factorial, you are doomed to use induction somewhere). But indeed this is not a proof by induction in the sense that one somhow tries to show $n!\le (\frac{n+1}2)^n\Rightarrow (n+1)!\le (\frac{n+2}2)^{n+1}$.
Oct
12
comment Proving that $n!≤((n+1)/2)^n$ by induction
As a sidenote: A direct proof without using induction in this form is possible based on the arithmetic-geometric-mean inequality, noting that $k\cdot(n+1-k)\le \left(\frac{n+1}2\right)^2$. The obstacle with an induction proof is that (while the step from $n!$ to $(n+1)!$ is easy - just multiply by $n+1$, this is not easy for the step from $(\frac{n+1}2)^n$ to $(\frac{n+2}2)^{n+1}$
Oct
12
comment Evaluating $\int _{-1}^{e} \frac{1}{x}dx$
Also, in complex-analysis you must specify along which path you integrate
Oct
12
answered If arrivals are not occuring at random, why do arrival times still have a probability distribution?
Oct
12
answered $4$ and $a_{2n + 1}$ are coprime?
Oct
12
answered How to find the point on a parabola where x and y are equal?
Oct
11
reviewed Leave Open $\lim_{x\to0^{+}} x \ln x$ without l'Hopital's rule
Oct
11
answered Understanding why removing two points from the 3-sphere ($S^{3}$) is homeomorphic to $S^{2} \times I$
Oct
11
comment Prove that $\tau(n) \leq 2\sqrt{n}$
You can replace $\le$ with $<$.
Oct
11
revised Proving that a discrete valuation-like function $w: \mathbb{Z}\backslash\{0\} \rightarrow \mathbb{N}$ is a $p$-adic valuation
added 221 characters in body
Oct
11
answered Proving that a discrete valuation-like function $w: \mathbb{Z}\backslash\{0\} \rightarrow \mathbb{N}$ is a $p$-adic valuation
Oct
11
comment Finite subsets and the Definable Power Set Operation
I don't know the book, but wonder: Does finiteness of $X$ imply that we "know" $n$?