106,455 reputation
696194
bio website von-eitzen.de/math/tntrep.xml
location Bonn, Germany
age 48
visits member for 1 year, 11 months
seen 4 hours ago

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


6h
answered What fraction of sunlight could we deliberately block out with an occulter?
8h
comment Find the Prize With a Limited Number of Questions
Note that (even if your second question should depend on the answer to the first), there are only four possible outcomes yes/yes, yes/no, no/yes, no/no from whicho you want to distinguish betwen five cups.
8h
comment On the indivisibility of odd perfect numbers by small numbers
Of course, such integers are known: $2,4,6,\ldots$ ;)
8h
answered Determine whether the function floor(x) is big omega of x
8h
answered Prove that $G$ has a element whose order is least common multiple of $m$ and $n$.
9h
answered Is this modified coffee cup equivalent to some n-fold torus?
10h
comment If an inequality is true for all natural numbers, is it necessarily true for all real numbers inbetween?
BTW, $\forall n\in\mathbb N_0,\forall x\in[-1,\infty)\colon (1+x)^n\ge 1+nx$ (note that one of the quantifiers is already about real numbers!) is already a counterexample: With $n=\frac12$ we do not have $\sqrt{1+x}\ge1+\frac12x$ for all$x\ge -1$. For example $\sqrt{1+48}=7<25=1+\frac{48}2$.
10h
comment If an inequality is true for all natural numbers, is it necessarily true for all real numbers inbetween?
A strict version would be $5x^2+1>5x$
11h
comment If A and B are disjoint finite sets, use induction on $|B|$ to show that $|A \cup B|$ is finite.
Which definition of finite do you use? Existence of bijection with an element of $\omega$?
11h
revised What's the proof for the #integers less than $n$ that can be expressed as the sum of two squares is $\frac n{\sqrt{\log n}}$?
edited title
14h
comment Radius of convergence of series given radius of convergence of another series
There is no such theroem as "For any power series the raidus of convergence is given by $\lim\frac {a_n}{a_{n+1}}$." You cannot assume thet $\lim \frac{c_n}{c_{n+1}}$ exists - think of $c_n=1+(-1)^n$. Go for $\limsup\sqrt[n]{|a_n|}$.
14h
comment Radius of convergence of series given radius of convergence of another series
You cannot apply the ratio test in general.
22h
comment Programming string in math
Of course the string occuring in print "Hello world!" hardly reminds us of free monoids ...
23h
comment Why can we make this integral change of limits? Is it obvious?
Compare with $\int_a^b f'(x)\, \mathrm dx=f(b)-f(a)=\int_{f(a)}^{f(b)}\mathrm dx$.
1d
comment How to find $f$ and $g$ if $f\circ g$ and $g\circ f$ are given?
You wrote "Since both the compositions are polynomials, it is clear that $f(x)$ and $g(x)$ also will both be polynomials in $x$." I gave an example of nonpolynomial $f,g$ with polynomial compositions. Even though they differ from the given polynomial, this counterexamlpe shows that it is certainly not "clear".
1d
comment How to find $f$ and $g$ if $f\circ g$ and $g\circ f$ are given?
It is not clear that $f,g$ will be polynomials! If $f\circ g$ and $g\circ f$ are the identity (polynomial), then $f$ can be any bijection and $g$ its inverse.
1d
comment Why do we still do symbolic math?
Even to formulate the algorithms that perform numerical computations, you need symbolic notation to develop/explain/understand them in the first place.
1d
answered $O(n \log k)$ for merging of $k$ lists with total of $n$ elements
1d
comment Fun quiz: where did the infinitely many candies come from?
We notice that $B$ cannot betreated as a black box. Also one needs to be careful what kind of limit process is to be used. We may assume that a certain candy is in a certain place at time 1 iff it is involved in only finitely many movements and its final place is the one assigned during that movement. The number of objects in a container is a secondary effect, the primary effect is the set of objects in the container. This is ok because the result of infinitely many additions/subtractions won't be defined in the first place.
1d
answered Number of edge disjoint Hamiltonian cycles in a complete graph with even number of vertices.