110,373 reputation
6101205
bio website von-eitzen.de/math/tntrep.xml
location Bonn, Germany
age 48
visits member for 2 years
seen 16 mins ago

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


Aug
25
answered Equivalence of ordered field and an order relation
Aug
25
answered derivative of $x\cdot|\sin x|$
Aug
25
answered Countable Set & Formal Grammar
Aug
25
comment Countable Set & Formal Grammar
Is $\Sigma$ really arbitrary or shouldn't we assume it is countable?
Aug
25
answered Equality of cardinality of $\mathbb{N}$ and $\mathbb{N} - \{0\}$
Aug
24
comment Explaining why $0,1\in S$
Since $(\cdot,\cdot)$ is sesquilinear, you even have $\mathbb R\subseteq S$ (and for all but trivial cases, $S=\mathbb R$)
Aug
24
comment Equivalence of ordered field and an order relation
A better statement would be: ${<}\mapsto \{\,x\in K\mid 0<x\,\}$ is a natural bijection between order relations with (a),(b),(c),(d) on $K$ and subsets $P$ of $K$ with $P+P\subseteq P$, $P\cdot P\subseteq K$, $K=P\cup\{0\}\cup {-P}$. So yes, if there are several $P$ possible, then there are also several $<$ possible and vice versa
Aug
24
answered $(A\cap B)C=AC\cap BC$ in an infinite group
Aug
22
answered Find the values of $f(0)$, $f(4)$, $f(6)$ and $f(18)$
Aug
22
comment General formula for $\frac{a^{2n+1}-a^{2n-1}}{a^n-a^{n-1}}$. Is such proof correct?
$a\ne 0$ is only needed if $n\ne 1$
Aug
22
comment General formula for $\frac{a^{2n+1}-a^{2n-1}}{a^n-a^{n-1}}$. Is such proof correct?
Compare yor result with lab's answer
Aug
22
comment General formula for $\frac{a^{2n+1}-a^{2n-1}}{a^n-a^{n-1}}$. Is such proof correct?
Why do you think that division is not a proof? -- But also: Did you notice which values of $a$ are forbidden (for the statement as such, so both kinds of proof are affected)? -- And finally, your result and proof do not match the problem statement
Aug
21
comment Notation problem in integration: write $dx$ or ${\mathrm{d}}x$?
Actually, I prefer $\int f(x)\,\mathrm dx$. :)
Aug
21
answered The number of divisors of any positive number $n$ is $\le 2\sqrt{n}$
Aug
21
revised What's time complexity of algorithm for “Word Break”?
added 204 characters in body
Aug
21
answered What's time complexity of algorithm for “Word Break”?
Aug
21
answered Is it true that a field is a vector space over a field?
Aug
21
comment Is infinite product of groups also a group?
A product of groups $G_i$, $i\in I$, is a group $G$ together with homomorphisms $\pi_i\colon G\to G_i$ such that for any group $H$ and homomorphisms $f_i\colon H\to G_i$ there exists a unique homomorphism $h\colon H\to G$ such that $f_i=\pi_i\circ h$ for all $i\in I$. Then: Yes, products exist in the category of groups. See mesel's answer for a reference, Vera's answer for an explicit construction.
Aug
21
comment Is this polynomial equation solvable? $ \alpha x^{n+2} + \beta x^{n+1} + \gamma x^3 + \delta x^2 + \epsilon x + \zeta = 0 $
For large $n$, $x_0=-\beta/\alpha$ is a good starting point for numerical methods.
Aug
21
comment The process of solving the inequality $\frac{8}{19} x\ge -1$
If you follow the next steps, you should see that by choosing $\frac{19}8$, the coefficient $\frac 8{19}$ gets happily cancelled. This would not happen with $\frac8{19}$ or any other multiplier.