4,226 reputation
21749
bio website bruno.stonek.com
location Montevideo, Uruguay
age 25
visits member for 3 years, 11 months
seen 1 hour ago

Math student at Université Paris 13.


Jul
12
asked Models of hyperbolic geometry
Jul
12
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.
Jul
11
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.
Jul
11
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..
Jul
11
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.
Jul
11
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
Jul
9
comment Why isn't the perfect closure separable?
Thank you for some great insight !
Jul
8
revised Problem in understanding set theory
added 137 characters in body
Jul
8
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...
Jul
8
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).
Jul
8
revised Problem in understanding set theory
added 361 characters in body
Jul
8
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".
Jul
8
revised Problem in understanding set theory
added 85 characters in body
Jul
8
answered Problem in understanding set theory
Jul
6
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
Jul
3
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.
Jun
27
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.
Jun
26
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.
Jun
26
comment Reference request: is mathematics discovered or created?
Thank you all for your research on such an informative answer!
Jun
26
comment Why isn't the perfect closure separable?
I had forgotten to bring the answer here! Better late than never...