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I'm a student of mathematics in Germany.


6h
comment What's the definition of a “local property”?
I think they are not equivalent in general. But I agree with you in that I prefer definition (3) over the others.
6h
comment What's the definition of a “local property”?
Good answer! Sadly, the second description of how “locally” is used and understood isn’t always applicable: Many topologists think of a locally compact space as one with each point having a compact neighbourhood, not an entire local base of compact neighbourhoods.
1d
comment So bad at maths sometimes I feel depressed about it
“You will always find someone who knows more math than you, and this is ok. This goes for all of us.” – I think this is false by Zorn’s lemma or something.
1d
comment So bad at maths sometimes I feel depressed about it
For the emotional part of your situation: Nothing’s lost, I think. I wouldn’t worry too much. Don’t be embarassed, don’t feel ashamed, don’t feel bad: Everything’s fine. For the actual advice on studying calculus: I don’t know.
1d
comment Prove that this element is nonzero in a tensor product
Just mentioning it because I needed a moment to see exactly how your answer applies to the question.
2d
comment iPod Shuffle question
Please replace "iPod" by "MP3 player" or "tracklist".
2d
comment Prove that this element is nonzero in a tensor product
If you use flatness of $ℚ$, then it already suffices to say $ℤ → \prod_{n ∈ ℕ} ℤ/nℤ$ has trivial kernel for $\bigcap_{n ∈ ℕ} nℤ = 0$, so tensoring by $ℚ$ we get an injective map $ℚ \otimes_ℤ ℤ → ℚ \otimes_ℤ \prod_{n ∈ ℕ} ℤ/nℤ$.
2d
revised Proving that a function is absolutely monotonic on a given interval
added 3 characters in body
2d
comment Extending a uniformly continous function to the closure of its domain
By “closer” you mean “closure”, right?
Dec
14
comment Are the polynomial functions on $S^1$ dense in $C(S^1,ℂ)$?
You don’t need Morera’s theorem, but only Cauchy’s integral theorem, do you? Or am I missing something? Anyway, really nice proof, I appreciate it a lot! Edit: Oh, from your last paragraph, it is actually clear that you understand Morera’s theorem to be the equivalence.
Dec
14
accepted Are the polynomial functions on $S^1$ dense in $C(S^1,ℂ)$?
Dec
14
asked Are the polynomial functions on $S^1$ dense in $C(S^1,ℂ)$?
Dec
14
comment Can $ℂ$ be viewed as a (nontrivial) field of fractions?
@MartinBrandenburg I should have written “nontrivial”. I wanted to avoid “Yeah, well $S = ℂ$.” but I feared there might be some other nontrivial subrings I overlooked which are equally pointless, so I wrote “interesting”. The answer given by Hurkyl is absolutely satisfactory to me.
Dec
14
accepted Can $ℂ$ be viewed as a (nontrivial) field of fractions?
Dec
14
comment Can $ℂ$ be viewed as a (nontrivial) field of fractions?
@Sal: Why not? Since the continuation of the $p$-adic absolute value has to be unique for algebraic extensions of $ℚ_p$, it makes sense to define a continued $p$-adic absolute value on the algebraic closure $\overline{ℚ_p}$. Because this value defines the metric on $\overline{ℚ_p}$, it has to be uniformly continuous and can therefore be extended to its own metric completion. The metric on the completion is still an ultrametric and so the ring given by Hurkyl is still a valid ring whose field of fractions must be all of $ℂ_p$.
Dec
14
comment Can $ℂ$ be viewed as a (nontrivial) field of fractions?
Can we extend this to the reals as well? Is $S' = O_ℂ ∩ ℝ$ a subring with $ℝ = Q(S')$ (where $O_ℂ = \{z ∈ ℂ;~|z|_p ≤ 1\}$)?
Dec
14
asked Can $ℂ$ be viewed as a (nontrivial) field of fractions?
Dec
13
comment Finding polynomial generators in a subspace
I edited your tex code. Let me know/unedit if it doesn’t fit with your intentions. What is $x$? Which base field are you considering, $ℝ$, $ℂ$? Does $\mathrm{gen} A$ denote the span of $A$ for that base field? Is $P_3$ the space of polynomials of the degree (exactly) $3$ over the base field? You should clarify.
Dec
13
revised Finding polynomial generators in a subspace
cleaned up tex code
Dec
13
answered How to figure out Laurent series expansion for $z^2 \sin(1/(z+i))$?