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476164
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location Buenos Aires, Argentina
age 21
visits member for 2 years, 8 months
seen 50 mins ago

(My avatar is a piece by artist Pollock named "Number 8".)

Some interesting questions, with great answers:

  1. The so-called Axiom of Choice

  2. Real numbers and sets

  3. How discontinuous can a derivative be?

  4. Why is summation by parts important? This is one example.

  5. Amazing work


6h
comment Is there a formal proof of this basic integral property?
@Jared Careful. You don't need continuity, but integrability. The good way to put it is, $$\int_a^b f=\int_a^c f+\int_c^b$$ whenever two of the integrals exist.
14h
comment Lebesgue Dominated Convergence: Alternative Proof?
What are you trying to prove? Use words, please.
16h
awarded  Enlightened
17h
awarded  Nice Answer
1d
comment Remmert, exercise 5, chapter 7 section 3. Theory of Complex Functions.
The book hasn't presented Laurent series so far. This is actually after showing every holomorphic function over a domain $D$ admits a powerseries development around each point of $D$. I was thinking about using that the $a_n$ are given by an integral and juggling with that, but I don't know how to proceed.
1d
comment Are we really ever plotting in polar coordinates?
You can plot a ray to infinity (the $r$ axis) and draw some circles around its starting point. Then you're looking at a polar coordinate chart of some sorts.
1d
comment What are the minimum conditions for the tangent plane to a surface to be defined, the chain rule to work, and directional derivatives?
I should've said "the differentials" "$Df(a)$, $Dg(f(a))$.
2d
asked Remmert, exercise 5, chapter 7 section 3. Theory of Complex Functions.
2d
comment how can i prove $\sum |a_i||b_i|\le(\sum |a_i|)|b|$?
Presumably $|b|=\sup |b_i|$.
2d
comment What are the minimum conditions for the tangent plane to a surface to be defined, the chain rule to work, and directional derivatives?
Can you define what you mean by a surface being differentiable at a point? The chain rule works whenever the derivatives exist (have you seena proof?). Directional derivatives may exist a every point without the function being continuous at the point.
Sep
19
comment Calculate D(f o g)(1,2)
The chain rule says that $D(f\circ g)(x)= Df(g(x))\circ Dg(x)$.
Sep
19
answered Prove that $d_n$ is a Cauchy sequence in $\mathbb{R}$
Sep
17
revised Why is the set of points where a complex polynomial does not vanish connected?
edited title
Sep
17
comment The perimeter of the rectangle is $20$, diagonal is $8$ and side is $x$. Show that $x^2-10x+18=0$
Please avoid subjective titles. Instead, consider giving your posts informative and objective titles.
Sep
17
revised The perimeter of the rectangle is $20$, diagonal is $8$ and side is $x$. Show that $x^2-10x+18=0$
edited title
Sep
17
comment Wicked domain of integration in a triple integral
What are you trying to integrate over this? Note the domain is symmetric in all variables.
Sep
17
awarded  proof-writing
Sep
17
comment Showing that $(\mathbb{R} \setminus \{ 0 \}, \, \times) \not \cong (\mathbb{C} \setminus \{ 0 \}, \, \times)$
Suppose that $x\neq 1,0$. If $|x|>1$; $x^4>|x|>1$. If $|x|<1$, $x^4<|x|<1$.
Sep
17
answered Why is this set connected?
Sep
16
comment What does “s.t.” mean?
(sometimes they use it as "sucht that" as in $\{x: {\rm s.t.\;\; blah})$