Recent content by Bacle2

Maybe a more direct way would be : ## x \in A ## iff ## x \in B ##.

A boundary is just a sort of "kink" in the manifold, so that near the boundary point the manifold is not locally like R^n. But I agree with lavinia; to get more out of an answer, it helps if you read the def first and ask something more specific.

Well, one issue is the independence of integration of forms on the choice of coordinates, which is not the case for functions.

Basically, P.O.U's allow you to patch locally-defined objects, like Riemannian metrics in the manifold into globally defined objects.

But 3.1416 is a better approximation to 3.1415927... than 3.1415. Maybe the better thing about 3.1415 is that it can be extended into a better approximation.

I was literally one of just two people at the movie theater tonight ( the 2nd person did not come with me). I felt like saying to him/her "you're in my seat", but I didn't know how it would be received.

Yes,good point, maybe were relatively early into the information age and we do not yet have good-enough data mining, both at a personal and industrial/institutional level.

Actually, the way I define it, the issue is not too much information, but too much noise. I define information on topic x to be anything that reduces the options/alternatives on determining a quality about x and different statements provide different measures of information on x. Example...

Strictly speaking s/he stated that the message may have been edited by a mentor/staff, that s/he did not clearly remember whether this was the case or not I don't see what is wrong here. Was your message distorted somehow by this edit? What part was edited-in, do you know; can you show it? I...

I actually agree with WWGD in that the only way of having a reasonably-level playing field between those with few resources and those with plenty is to ignore copyright _until_ one moves up in the professional ladder. After that, no more freebies. And it is absurd that countries with...

It would be nice if the OP could be more specific about the vector space s/he is working in; gummz, can you tell us more about what space you are working in? are g,h part of a basis for the space?

And how about the trick of dividing by 2 and appending a zero when multiplying by 5 ? This is just because 5 =10/2. Say you want to find 36 x 5 . Then 36/2 =18 and 18 x 10 =180. By the same trick, dividing by 5 is multiplying by 2 and appending a zero : 240/5 240 x2 =480 , 480/10= 480.

Can the depth be different from R when the curvature is constant, with value 1/R; I would have thought the bowl would have to be a hemisphere (so that the vertical distance from rim to base would then be R) ; in this case the lower hemisphere. Am I missing something here?

But, if the curvature is constant, with value 1/R, can the depth then be greater than R? Maybe I misunderstood?

Set up a right triangle with sides x and 4, so that the tangent of one of the angles is x/4, i.e., tanθ=x/4. Then θ=tan^{-1}(x/4) . From the drawing, figure out the value of sinθ.