3,196 reputation
1833
bio website jakitoimgeisterhaus.blogspot.…
location Munich, Germany
age 38
visits member for 3 years, 1 month
seen 22 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.


Jul
22
comment Why are box topology and product topology different on infinite products of topological spaces?
@MathsLover The set theoretical topological spaces where defined by Felix Hausdorff in his book "Grundzüge der Mengenlehre", which appeared in 1914. In 1912, Jan Brouwer had started intuitionism, but Felix Hausdorff's work is not really based on it. The linked publication page of Dirk van Dalen is a good source for the connections between formal intuitionistic logic and topological spaces. If the links in that page don't work in your browser, copy the desired "link address" and replace "papers.html" in the current addresss by "articles/..." from the copied "link address".
Jul
20
answered Why are box topology and product topology different on infinite products of topological spaces?
Jul
18
comment Can a biased physical random source be post-processed to control the bias?
@Did Thanks, now I see where I made a mistake in the description of the method. Should be fixed now. This also answers part of my initial confusion, i.e. why I asked this sort of questions in the first place.
Jul
18
revised Can a biased physical random source be post-processed to control the bias?
OK, now I see my mistake in the description of the method
Jul
18
comment Can a biased physical random source be post-processed to control the bias?
@Did You mean I made a mistake in my description of the procedure? Or you mean you simply don't believe that such a can procedure work? Or is it just that you can't recognize the well known situation (produce unbiased random bits with the help of a single biased coin) behind my complicated and overly formal description?
Jul
17
revised Can a biased physical random source be post-processed to control the bias?
Thought a bit about how this problem can be pragmatically addressed, and modified question accordingly
Jul
12
comment Which natural number predicates can be defined in Robinson arithmetic?
My initial expectation for a function "definition" (and my statement "...exponentiation cannot be defined in Robinson arithmetic!") were based on the requirements for eliminating an additional function symbol in the non-logical language by a suitably defined predicate (i.e. a first order formula). But because Robinson arithmetic seems to be unable to prove totality, it seems like a good idea to omit the totality requirement. (After all, some logics also have terms and function symbols without existential import. Totality isn't a "Horn property" either...) I updated the question accordingly.
Jul
12
comment Which natural number predicates can be defined in Robinson arithmetic?
Here is an explicit formula for $E(x,y,z)$. It's only 6 lines, but it uses abbreviations/auxiliary predicate definitions. But I agree that even if these abbreviations would be expanded, the resulting formula would still not be that complicated.
Jul
12
revised Which natural number predicates can be defined in Robinson arithmetic?
Now I understood the point which Asaf and Peter raised...
Jul
12
comment Which natural number predicates can be defined in Robinson arithmetic?
@hardmath I tied to clarify this now. It turns out that I just want to know whether transitivity, reflexivity and antisymmetry can be proved for a suitable definition (by a first order formula in $Q$) of $x\leq y$. I'm quite convinced that this isn't possible for the definition given in the question, so either one has to come up with a definition for which this can be proved, or show that no such definition can exist.
Jul
12
revised Which natural number predicates can be defined in Robinson arithmetic?
Added the requested clarification
Jul
12
asked Which natural number predicates can be defined in Robinson arithmetic?
Jul
10
revised Can a biased physical random source be post-processed to control the bias?
edited tags
Jul
10
reviewed Close Proof that arithmetic mean is greater than geometric mean?
Jul
10
revised Can a biased physical random source be post-processed to control the bias?
edited tags
Jul
10
asked Can a biased physical random source be post-processed to control the bias?
Jul
7
comment Which biased random sources can be obtained from an unbiased one?
The expanded answer is even more awesome. And it is actually a quite canonical procedure, in a certain sense.
Jul
7
comment Which biased random sources can be obtained from an unbiased one?
Cool, I'm glad I asked. But you surely mean one can get every $p\in \mathbb Q\cap[0,1]$, not every $p\in[0,1]$. Or what would you do for $p=1/\sqrt{2}$?
Jul
7
accepted Which biased random sources can be obtained from an unbiased one?
Jul
7
asked Which biased random sources can be obtained from an unbiased one?