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bio website asmeurer.github.io
location Austin, TX
age 25
visits member for 4 years, 4 months
seen 17 hours ago

I am a software developer at Continuum Analytics. I am also the lead developer for the SymPy project.

Unless otherwise noted, all my answers on StackExchange, including code snippits, are released under ​Creative Commons CC0 (public domain).


Dec
18
suggested approved edit on Working out digits of Pi.
Dec
18
comment Working out digits of Pi.
One thing I'm not sure about: the mpmath source says that each term adds roughly 14 digits, but it's not clear if it's 14 more digits of $\pi$ or 14 more digits of $\frac{1}{\pi}$.
Dec
18
comment Working out digits of Pi.
This is an insanely inefficient way to calculate $\pi$. Even if you have a calculator and only want to calculate 10 digits or so, it will take you forever.
Dec
18
answered Working out digits of Pi.
Dec
18
comment Which one result in mathematics has surprised you the most?
I'm not familiar with the wrapping proof. Is that the same as this?
Dec
18
comment Which one result in mathematics has surprised you the most?
${}{}{}{}{}{}x^3$?
Dec
18
comment Which one result in mathematics has surprised you the most?
Also known as $\sqrt{\pi}$.
Dec
18
accepted Is there a fundamental reason that $\int_b^a = -\int_a^b$
Dec
18
comment Is there a fundamental reason that $\int_b^a = -\int_a^b$
"The fundamental theorem of calculus...is based on this interpretation of the integral." This, I think, is the key insight here.
Dec
18
comment Is there a fundamental reason that $\int_b^a = -\int_a^b$
But what about signed measures?
Dec
18
comment Is there a fundamental reason that $\int_b^a = -\int_a^b$
Your very last sentence also gives a very nice motivation (it's ultimately the same as the accepted answer from math.stackexchange.com/questions/232455/…). I need to think on how this can apply to summations.
Dec
18
comment Is there a fundamental reason that $\int_b^a = -\int_a^b$
"...and $\int_A f+\bar\int_A\,f=0$." As you've defined it, how could this not hold?
Dec
18
awarded  Nice Answer
Dec
18
comment Is there a fundamental reason that $\int_b^a = -\int_a^b$
I'm not sure we're understanding each other. What I'm saying is that a summation is a Lebesgue integral with the counting measure.
Dec
18
comment Is there a fundamental reason that $\int_b^a = -\int_a^b$
Ah, that's a good reason. But I'm especially curious if this can be explained for Lebesgue integrals, since summations are special cases of Lebesgue integrals, not Riemann integrals (or at least not as far as I know).
Dec
18
revised Is there a fundamental reason that $\int_b^a = -\int_a^b$
Fix Karr's convention for summation
Dec
18
comment Is there a fundamental reason that $\int_b^a = -\int_a^b$
@CameronBuie that question doesn't really give the answer I'm looking for. At least to me, integrals are Lebesgue integrals (especially if I want to consider sums as special cases of integrals), and things like the fundamental theorem of calculus don't always hold, at least not without some generalized definitions of derivatives.
Dec
18
asked Is there a fundamental reason that $\int_b^a = -\int_a^b$
Dec
18
answered What exactly is infinity?
Dec
17
comment Purely “algebraic” proof of Young's Inequality
I thought the point here was to find them to prove the inequality. Artin's theorem tells us that our search is a reasonable direction to take (and that purely algebraic proofs are possible, at least modulo choosing rational exponents only).