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.

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...

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.

What do you mean by the units of R, how do you define the dual of a ring? Do you define the ring as a module over itself and then define its dual?

Just work Mod7 .

I liked "Shutting out the Sun" , by Michael Zielenzinger, about post 90's Japan, when it sort-of imploded. The book explores Japanese society from the perspective of the social phenomenon of the "Hikikomori"; children who live at home (they literally stay at home, even for years at a time; their...

This is mostly a philosophy question, so that I don't believe it has a clear yes/no answer. There are many good books on it; some good ones are the "What is Mathematics", and many of the books by Ian Stewart. Antonio Damasio, a Neurologist ( or some type of brain scientist) put out a good book...