Reputation
4,840
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
1 18 38
Newest
 Nice Answer
Impact
~166k people reached

Apr
15
comment Does the sequence $x_{n+1} = \frac{1}{2} ( (x_n)^2 + c ) $ diverge?
The sequence is not necessarily strictly increasing as you claim. Consider $x_0 = \frac32$ and $c= \frac14$, then $x_1 = \frac{11}8 < \frac32$. For these initial conditions the sequence is strictly decreasing and bounded below by 0, so it is convergent.
Apr
5
awarded  Nice Answer
Mar
20
awarded  Yearling
Mar
1
revised Why aren't integration and differentiation inverses of each other?
replaced ~ with \sim since apparently the former doesn't work in MathJax
Feb
29
revised Why aren't integration and differentiation inverses of each other?
added a couple paragraphs on IVPs
Feb
28
comment Why aren't integration and differentiation inverses of each other?
@goblin I suppose I was unclear, but I was looking for cases in which the derivative was an automorphism, not merely an isomorphism. You'll notice that both the domain and range of your construction are naturally embedded in the one I did in "option 1" in such a way that they are compatible with the derivative, and indeed this is the smallest such space with that property on which the derivative is invertible. But yes, given the importance of initial value problems, this approach does deserve a mention somewhere, so I'll edit something in soon.
Dec
24
awarded  Guru
Nov
23
comment Weyl transformation of geodesic distance
Are you sure you want to look at arbitrary Weyl transformations? If so, then the problem is hopeless as Willie Wong suggests. But If you're doing things related to CFTs, usually the only Weyl transformations which really matter are those induced by conformal maps. That's a much smaller class; arbitrary Weyl transformations form an infinite dimensional group isomorphic to $C^\infty(M)$, but for example on Minkowski space, the "conformal group" (in the standard physics terminology) is 15 dimensional, with a 10-dimensional Poincare subgroup which preserves the metric.
Jul
30
awarded  Enlightened
Jul
30
awarded  Nice Answer
Apr
12
awarded  Enlightened
Apr
12
awarded  Nice Answer
Mar
20
awarded  Yearling
Jan
5
awarded  Nice Answer
Jan
2
awarded  Good Answer
Jan
1
revised Why aren't integration and differentiation inverses of each other?
copy-editing
Dec
28
awarded  Guru
Dec
28
awarded  Enlightened
Dec
28
awarded  Nice Answer
Dec
28
revised Why aren't integration and differentiation inverses of each other?
some additions in part 2