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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.
Apr
6
awarded  Investor
Apr
6
comment “Differential” of a measure
Just a thought: can the formalism of generalised functions be somehow used to unify $dx$ and $d\mu$?
Apr
5
comment Negative Zero in the set of real numbers
But in any case i think that "equality" did not always mean "identity".
Apr
5
comment Negative Zero in the set of real numbers
Well, judging by the upvotes, i thought that there were some content in the question, and there were something to prove...