# Bruno Stonek

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bio website bruno.stonek.com location Montevideo, Uruguay age 25 member for 3 years, 11 months seen 1 hour ago profile views 1,985

Math student at Université Paris 13.

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 Jul12 asked Models of hyperbolic geometry Jul12 comment Problem from Halmos's Finite Dimensional Vector Spaces A note to your note: well, functionals are functions, in the usual set-theoretic meaning! So the notation $y(x)$ for a functional $y\in P'$ and a vector $x\in P$ is the same notation as ever. Jul11 comment What does {2x|P(x)} mean? meaning a priori, that is, unless the $x$ you are talking about are elements of a structure where "multiply by 2" makes sense: for example, the natural numbers $\mathbb{N}$, the real numbers $\mathbb{R}$, the continuous functions $\mathbb{R}\to \mathbb{R}$, etc. Jul11 comment What does {2x|P(x)} mean? I don't understand your objection (the latex in it was ill-rendered). Are you objecting to the use of $x\in \dots$? Think that a priori $2x$ doesn't have a meaning. For example, if $x$ is a color, such as red, what does $2x$ mean? It does have a meaning if $x$ is an element of some mathematical structure that admits to "multiply an element by 2", for example a monoid, a group, a ring, a field, a vector space... Thus, in general set theory, a set $\{2x: P(x)\}$ (note that I am using $:$ instead of $|$: it is different notation for the same thing, see Bill's answer below) does not have.. Jul11 comment What does {2x|P(x)} mean? @fahad: No, the order in which you check the propositions is not relevant: $\{y:\exists x (y=2x \wedge P(x))\}=\{y: \exists x (P(x) \wedge y=2x\}$. In other words, conjunction is commutative. Jul11 comment What does {2x|P(x)} mean? Just as a comment, you should be aware that a "collection of elements" described in such manner is not necessarily a set-- see e.g. en.wikipedia.org/wiki/Russell%27s_paradox . However, if in this case you are thinking of $x\in \mathbb{R}$, then this set exists, but to be sure it exists you should write it as $\{y\in \mathbb{R}: \exists x (x\in \mathbb{R} \wedge y=2x \wedge P(x))\}$ and use the fact that $\mathbb{R}$ exists and the comprehension axiom-- see: en.wikipedia.org/wiki/Comprehension_axiom Jul9 comment Why isn't the perfect closure separable? Thank you for some great insight ! Jul8 revised Problem in understanding set theory added 137 characters in body Jul8 comment Problem in understanding set theory Well, in your answer to 2), you're not really proving that it is never true that $A\subseteq B$, you're just giving an example where it is not true... Jul8 comment Problem in understanding set theory It would be necessary for you to specify under which set theory you are working. In my answer below I assumed you were dealing with Zermelo-Fraenkel (ZF). Jul8 revised Problem in understanding set theory added 361 characters in body Jul8 comment Problem in understanding set theory @Gerry: nicely put. I was going to comment it in this form: "A bag is not the same as a bag containing a bag". Jul8 revised Problem in understanding set theory added 85 characters in body Jul8 answered Problem in understanding set theory Jul6 comment Equivalent conditions for a preabelian category to be abelian Part 3 is proven in your comments above, and it is perfectly fine. Here is a proof which does not use that the coimage of an epimorphism is the same morphism. Let $f:A\to B$ be mono-epi. Then $f=ker g$ for some $g:B\to X$. Then $gf=g(kerg)=0=0f$: since $f$ is epi this implies $g=0$. But then $f=ker g=ker 0=Id_B$ hence $f$ is an isomorphism. @Theo Jul3 comment $i^2$ why is it $-1$ when you can show it is $1$? See: en.wikipedia.org/wiki/… , where there are other false proofs of this kind. Jun27 comment Ways to evaluate $\int \sec \theta \, \mathrm d \theta$ @Mariano: I'm quite late to the party here, but would you care to elaborate? I'm not quite sure I understand what you mean by "rational parametrization of the unit circle" and how it's related to Weierstrass substitution. Jun26 comment Reference request: is mathematics discovered or created? @Theo: Thank you! No, I can't see deleted answers. I will surely check it out. The encyclopedia entry looks very interesting: I don't know if it deals with the subject at hand, but in any case it seems it will be a very illuminating reading. Jun26 comment Reference request: is mathematics discovered or created? Thank you all for your research on such an informative answer! Jun26 comment Why isn't the perfect closure separable? I had forgotten to bring the answer here! Better late than never...