3,377 reputation
1937
bio website jakitoimgeisterhaus.blogspot.…
location Munich, Germany
age 38
visits member for 3 years, 6 months
seen 2 hours ago

My past research interests included differential algebraic equations, nonlinear analysis and relations between symmetries and structural properties.

I recently investigated hierarchical structures, starting from group cohomology, continuing with semi-group theory and ending with lattices and universal algebra.


Oct
31
answered Can the b-adic representation of rational numbers (by quote notation) be extended to non-terminating expansions?
Oct
30
reviewed Approve How to prove this inequality $\frac{a_{1}a_{2}+a_{2}a_{3}+\cdots+a_{n-1}a_{n}}{a^2_{1}+a^2_{2}+\cdots+a^2_{n}}\le\cos{\frac{\pi}{n+1}}$
Oct
30
reviewed Approve Orbit-Stabilizer Theorem
Oct
30
comment Can the b-adic representation of rational numbers (by quote notation) be extended to non-terminating expansions?
I also thought about this. My only worry was that the $p$-adic metric is induced by an absolute value (i.e we have $|xy|_p=|x|_p|y|_p$), but the combined norm only satisfies $|xy|\leq|x||y|$. So I wonder whether this is enough to ensure that the completion is a field.
Oct
30
comment Can the b-adic representation of rational numbers (by quote notation) be extended to non-terminating expansions?
I see a potential problem now, if I only check whether the arithmetic operations are well defined: After the addition of two numbers in the representation, one of the $\beta_i$ might go towards infinity. Hence the result must be set to zero. Which is fine in a certain sense, but associativity (and distributivity) of addition might be lost (not sure whether this can happen). So in addition to being well defined, I also have to check that addition is associative and distributive.
Oct
30
asked Can the b-adic representation of rational numbers (by quote notation) be extended to non-terminating expansions?
Oct
28
awarded  Revival
Oct
16
reviewed Approve coordinate geometry high level problems
Oct
7
reviewed Approve infinitely many solutions to $\displaystyle x^n + y^n = z^{n+1}$
Oct
7
comment Are higher order logics substantially stronger than second order
In a certain sense, this answer is only true if the other axioms ensure that there are infinitely many objects/elements in the universe. And if the other axioms already ensure that we have the consistency strength of bounded Zermelo set theory or ZFC set theory, then just adding higher order variables and impredicative comprehension axioms (without using higher order variables in some of the other axioms) won't increase consistency strength any further.
Oct
6
revised Are higher order logics substantially stronger than second order
Oh, I forgot that I wanted to say something about the last word property
Oct
6
answered Are higher order logics substantially stronger than second order
Oct
5
revised Is multiplication in mixed radix numeral systems complicated?
edited tags
Oct
4
asked Is multiplication in mixed radix numeral systems complicated?
Sep
30
awarded  Explainer
Sep
28
comment Why are real numbers useful?
Nice answer, but when you say "And the wanted this line to be with no gaps, to be a continuum," what do you mean by "no gaps"? The rational numbers have no gaps either, in a certain sense. In another sense, the real numbers have gaps too, for example if you look at them as a subset of the surreal numbers. I think instead of the unclear "no gaps", what they really wanted was "completeness" (not necessarily limited to the order) and the Archimedean property: $\forall x\in {\mathbb R} \quad \exists n\in {\mathbb N} \quad x < n$.
Aug
18
answered How much maths can we do in NF(U)?
Aug
17
revised Why learn to solve differential equations when computers can do it?
fixed links
Aug
16
answered Why learn to solve differential equations when computers can do it?
Aug
15
revised Which natural number predicates can be defined in Robinson arithmetic?
edited body