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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...
Jun
26
accepted Why isn't the perfect closure separable?
Jun
26
answered Why isn't the perfect closure separable?
Jun
26
comment Reference request: is mathematics discovered or created?
@Theo: thank you for your confidence.
Jun
26
comment Reference request: is mathematics discovered or created?
@Pete: But Pete, I'm not asking for help in writing the text, not at all. I'm just asking for useful references. What I'm supposed to compose will not be comprised merely of a bibliography. I don't see how this is unethical, if that's what you're implying.
Jun
25
comment Reference request: is mathematics discovered or created?
...proper "philosophy of math/science" or "epistemology" course available. So if I have to do some work for a course that doesn't interest me much and is just compulsory, I might as well do it in something that interests me, is what I think.
Jun
25
comment Reference request: is mathematics discovered or created?
@Pete: it is not a research paper what I have to write (if I understand well what you mean by "research paper"), just a 10-15 pages survey on some topic of interest. To be honest, the course is not on philosophy of science but rather on "university, science and society". Some of the early lectures were on the history of science and some epistemology; based on that I want to write something related to that part of the course, and not the more socially-oriented part which is not of great interest to me. In fact, I've matriculated to this course only because it is compulsory and there is no...