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seen Jul 18 at 21:39

Jul
5
comment Computation of the Frenet-Serret trihedron in $\Bbb L^3$ (Lorentz-Minkowski space)
Is the inner product of $N$ and $B$ really 1? I am currently under the impression that the $T,N,B$ system of coordinates is an orthonormal set that moves along the curve $\alpha$. If we know $T$ and we can then calculate $N$ as a derivative and then $B$ as $T\times N$?
Jul
2
awarded  Curious
Jun
24
comment If nonempty, nonsingleton $Y$ is a proper convex subset of a simply ordered set $X$, then $Y$ is ray or interval?
@BrianM.Scott example 3 on page 85 is the positive integers with order topology. Is this another example of a convex set with the property?
Jun
20
comment Real analysis with a non-standard topology
Hi Bryan, if I interpret your first paragraph correctly, analysis builds on some primitive topological set-up. My question is a little more specialized, suppose we start with a set say $\mathbb{R}$ and then construct two incomparable topologies on it. Do we have a feeling for what happens when we construct the rest of the required machinery on top of those two cases? In my example, do we get identical structures at completion with both the Sorgenfrey line and the standard topology? Will differences in the topology elicit a difference with metrics and linear structures?
Jun
20
revised Real analysis with a non-standard topology
edited tags
Jun
20
asked Real analysis with a non-standard topology
Jun
19
answered Finding Fixed Points for Coupled ODE
Jun
19
comment A Basic Truth of Set Theory?
Ok I think I see the reasoning: my statement about $\mathbb{R}$ is not well defined because what does one really mean by a union of elements?? Its a notion defined for sets. Intuitively though you might suspect what I want. The set $\mathbb{R}$ is equivalent to all its points.
Jun
19
comment Finding Fixed Points for Coupled ODE
If $X$ and $Y$ are both non zero, then there is a continuum of equilibria. Along the line $Y=N-X$.
Jun
19
comment A Basic Truth of Set Theory?
@ Thomas No special reason Tom.
Jun
19
comment A Basic Truth of Set Theory?
what if we take $X=\mathbb{R}$. Is it true then that the union over all the $x$ works out? Is there a class of sets where you don't need the singletons?
Jun
19
accepted A Basic Truth of Set Theory?
Jun
19
comment A Basic Truth of Set Theory?
@ Asaf its been a while since I looked at Halmos but this reminds me of it. thx
Jun
19
comment A Basic Truth of Set Theory?
ah, I see the issue. With this adjustment, is the statement taken on faith or provable by other means?
Jun
19
comment A Basic Truth of Set Theory?
edited it: Just for clarification why must we use the set containing x there?
Jun
19
revised A Basic Truth of Set Theory?
added 4 characters in body
Jun
19
asked A Basic Truth of Set Theory?
Jun
16
comment finite subset topology
@MPW yes that is what is intended here. ty
Jun
16
asked finite subset topology
May
21
comment how to find matrix A from complete solution to Ax=b
hint: $Ax$ is a linear combination of the columns of $A$.