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bio website von-eitzen.de/math/tntrep.xml
location Bonn, Germany
age 48
visits member for 1 year, 11 months
seen 2 hours ago

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

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.
comment Can someone explain this process? (Khan Academy)
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.
answered For a cubic equation, prove that two critical points of the same sign imply one root
comment Set of points of $[0,1)$ that have a unique binary expansion
Assume a number $x$ has two distinct expansions, first differing at the $n$th place. Then my multiplying with $2^n$ and subtracting an integer, you get two representations $0.a_1a_2\ldots$ and $1.b_1b_2\ldots$ of the same number. The latter is $\ge 1$, the former is $\le 1$, hence both must equal $1$, so they must be $0.1111\ldots$ and $1.000\ldots$. Thus one of the original representations for $x$ ends in all zeroes, i.e. is finite. But a finite 0-1-string (ending in $1$) can be viewed as a reversed representation of an integer, hence there are only countably many
answered Estimate bias of a coin
comment Do journals that published a proof of an important theorem $T$ publish another proof of $T$?
It's less about $T$ than about $P'$, you might say: A substantially new proof may use different (new?) methods, from which we can possibly learn more than from $T$ itself. Also, $P'$ may be so differnt that it may suggest different generalizations of $T$. You might even publish a new(!) proof of Pythagoras, adding to an already long collection.
comment Is there a general way to parameterize all implicit functions?
Depends on what you precisely mean by parametrizing. What about disconnected sets like $xy=1$?
answered Path Connectedness argument for $SO(n, \mathbb{R})$
answered What does linearly equivalent mean in this context
comment If $\operatorname{rank}(A)=n$ then $\operatorname{rank}(AB)=\operatorname{rank}(B)$
Well, if $n$ occurs in a matrix problem without further mention, I thought it safe to assume that $n=\dim V$ ...
revised A continuous bijection from a Hausdorff space to a non-compact space which is not a homeomorphism
added 353 characters in body
answered A continuous bijection from a Hausdorff space to a non-compact space which is not a homeomorphism
comment A continuous bijection from a Hausdorff space to a non-compact space which is not a homeomorphism
$\mathbb R$ with discrete topology?
answered If $\operatorname{rank}(A)=n$ then $\operatorname{rank}(AB)=\operatorname{rank}(B)$
answered Finding a condition on the real $a$ such that $P$ is divisible by $(x-a)^2$
comment How to simplify $(x+4)^2$?
The question remains: Is that a simplification?
comment I'm not understanding this puzzle
And it coul be "What number am I thinking of?"
answered existence of K_3 in a graph with n^2+1 edges
comment Gödel's ontological proof - How does it work?
How are the axioms motivated? None of them really persuades me.
comment How to bound the following sum
@Assaultous2 Yeah, for $i<\sqrt x$ we may consider $\{x/i\}$ and $\{x/(i+1)\}$ more or less random and independant. This brings us from $\le\sqrt x$ to $\approx \frac 38\sqrt x$ or so