Reputation
4,999
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
9 19
Newest
 Nice Answer
Impact
~82k people reached

May
19
answered How to prove the inequality $\Theta(x,y)\le \Theta(x,z)+\Theta(z,y)$?
May
18
answered Complex Exponents
May
18
answered Deduce plus and minus with Cross Product in 3th and 4th Maxwell equations
May
18
awarded  Commentator
May
18
comment Global conformally flat coordinates in 2d spacetimes
Dear @Dionigi, the Lorentzian-signature "disks" defined as any contractible manifolds can't be mapped to each other. Imagine that the shape is described by an equation involving $x^+,x^-$, the light-like coordinates. The conformal transformations in this case are separate reparametrizations of $x^+$ and of $x^-$. This is clearly not enough to relate all contractible shapes. For example, a null boundary of a "diamond" will always stay null under conformal transformations, and manifolds with piecewise spacelike and then timelike boundaries etc. will always have these pieces.
May
18
awarded  Nice Answer
May
18
awarded  Critic
May
18
comment Branch cut of the logarithm
Thanks for your comment, but when you mention an "answer", what is the question you're trying to answer?
May
18
comment Global conformally flat coordinates in 2d spacetimes
Apologies, I don't understand in what sense is $\Sigma \times {\mathbb R}$ a disk: isn't it a noncompact manifold?
May
18
answered Linear Algebra Question
May
18
revised Global conformally flat coordinates in 2d spacetimes
added 375 characters in body
May
18
revised Global conformally flat coordinates in 2d spacetimes
added 300 characters in body; added 4 characters in body; added 1105 characters in body
May
18
answered Global conformally flat coordinates in 2d spacetimes
May
18
answered Branch cut of the logarithm
May
18
answered Energy functional in Poisson's equation: what physical interpretation?
May
18
comment Why does $1+2+3+\cdots = -\frac{1}{12}$?
Dear @joriki, your "other" method is completely legitimate, too. You just have to avoid simple errors. You never get $\zeta(0)$ by the operations. In reality, $S-2S-2S=-3S$ is $1-2+3-4+\dots$ which is equal to $+1/4$ as shown both in Matt's and my answer. And indeed, that's $-3$ times $-1/12$. When summing the terms, you can't randomly "clump" the terms into pairs and give them wrong interpretations because such a manipulation distorts the values of $n$ from which the individual terms came.
May
18
comment Why does $1+2+3+\cdots = -\frac{1}{12}$?
Dear @joriki, I don't have a combative tone. I was just answering some questions, by the OP, and partly by others. All answers in mathematics ultimately boil down to some propositions' being right, which is equivalent to their negations' being wrong. This is not about combat. This is the basic point of maths - and all sciences, too. I could easily argue that it's combative for someone to question that $1+2+3+\dots = -1/12$ or that $2+2=4$. Well, I am not sure whether it's combative but it's incorrect.
May
18
comment Why does $1+2+3+\cdots = -\frac{1}{12}$?
The comments about the zeta function were added to the wording of the question a moment ago. As far as I remember, the original unedited question by perplexed didn't refer to the zeta function. Independently of that, I wrote that it was incorrect to say - as some of the comments did - that the zeta function regularization is the only way to show that the answer $-1/12$ was correct. It is not the only method and I have explicitly shown two additional ones in my answer. Most importantly, it is the correct value that has to be assigned to the sum whenever a finite sum has to be assigned.
May
18
revised Why does $1+2+3+\cdots = -\frac{1}{12}$?
added 914 characters in body; added 292 characters in body
May
18
revised Why does $1+2+3+\cdots = -\frac{1}{12}$?
added 153 characters in body; added 129 characters in body