Alexey
Reputation
472
Next privilege 500 Rep.
Access review queues
 Dec 19 awarded Nice Question Sep 4 comment Does forcing need a countable transitive model @AsafKaragila, isn't it necessary then to add to ZF some axiom that standard models exist? Aug 15 revised How do I show the existence of a weakly inaccessible cardinal is not provable in ZFC? to the best of my knowledge, "ö" spells "oe", so should be "Goedel" if written without diacritics Aug 15 suggested approved edit on How do I show the existence of a weakly inaccessible cardinal is not provable in ZFC? Jul 30 comment When are two proofs “the same”? I have stumbled upon a preprint Mathematical semantics of intuitionistic logic by Sergey Melikhov where this notion is mentioned as a motivation. I am reading it now. Jul 9 accepted How to call a category with a single morphism between every two objects? Jul 9 comment How to call a category with a single morphism between every two objects? @AdLibitum, i think that chaotic category (see the answer of Martin Brandenburg) sounds better. Jul 9 comment How to call a category with a single morphism between every two objects? @AdLibitum i would never call a trivial group or the empty set boring. Jul 9 comment How to call a category with a single morphism between every two objects? @AdLibitum, you do not call a group with a single element a boring group. Jul 9 asked How to call a category with a single morphism between every two objects? Jul 7 comment Matrix inverses - Why are they derived the way they are? This method is based on a property of determinant, namely on Laplace expansion. May 27 comment Self Teaching Theory for Olympiad. Need advice for books. I do not remember that math olympiads would require any special theory. It looked more like sport: just practice on problems of similar level. May 8 comment Some weaker axiom than “no nontrivial zero divisors.” Good point. I am mostly interested in a semigroup without $1$. May 8 revised Some weaker axiom than “no nontrivial zero divisors.” added 131 characters in body May 8 comment Some weaker axiom than “no nontrivial zero divisors.” Yes, i should maybe add an explanation (later). May 8 asked Some weaker axiom than “no nontrivial zero divisors.” Apr 9 comment Decomposition of ball in Banach Tarski paradox and covering a soccer ball I think the two parts are related: with just one soccer ball and Banach-Tarski Theorem one can start soccer ball company. Apr 8 comment “Differential” of a measure I agree however that the expression $f(x)dx$ can be generalized outside of the context of differential forms. For example, if $f$ is continuous and $g$ is of bounded variation on $[a,b]$, then $\int_a^b f(x)dg(x)$ is defined (no measure needed either). Apr 8 comment “Differential” of a measure If $g$ is continuous and $\mu$ is the Lebesgue measure, then $\int_{\mathbb{R}}g(x)d\mu =\int_{\mathbb{R}}g(x)|dx|$ (no orientation on $\mathbb{R}$ is needed for the second integral). The question remains: what is $g(x)d\mu(x)$? Apr 8 comment “Differential” of a measure @epimorphic, $g(x)dx$ is a differential form. To integrate it over $\mathbb{R}$, no measure is needed, only the differential structure (tangent spaces at each point of $\mathbb{R}$, etc.) and the orientation.