Thread: subspace of R^3 and some sequences.

1. could someone show me some subspaces of R^3 and some convergent sequences here.

note:we study on only bounded spaces.

thanks  2.

3. When you say bounded spaces, do you mean the space is closed under some operation?  4. Originally Posted by GiantEvil When you say bounded spaces, do you mean the space is closed under some operation?
both complete and incomplete types would be good here.
thank you  5. Hmm... Is mathematical nomenclature undergoing some linguistic drift?
Anyhow; http://www.math.jhu.edu/~nitu/subspace.pdf  6. Originally Posted by GiantEvil Hmm... Is mathematical nomenclature undergoing some linguistic drift?
Anyhow; http://www.math.jhu.edu/~nitu/subspace.pdf
to begin with responding your question, no , no such thing.
you remarked closure. and you are probably aware that any subspace is closed.

furthermore,I need some 3D graph and illustrations.(Non linear samples would be better) thanks for your shared post but the document that you provide is very very brief.

I need detailed instructions  7. R^3 by its nature is a linear space. Non linear examples in that space would be functions. The subspaces of some R^n would be all R^m such that m<n and m>0. Any vector space with a bound is not closed under either vector addition or scaler multiplication because the result of some operation might be outside the bound.

Try Googling “vector function”.  8. oh ,sorry for failure. I did not complete my sentence.I was to say ;

"any subspace will be complete when it is closed."

and a question :

can we create functional sequences which their elements are vector function each?

(I am deling with engineering projects and thus,I need examples as much as possible.)  9. Well, swimming in the deep water here. (See what I did there?)
Try here; https://en.wikipedia.org/wiki/Vector-valued_function  10. Originally Posted by GiantEvil R^3 by its nature is a linear space. Non linear examples in that space would be functions.
Try Googling “vector function”.
do we assess linearity only for "functions"?

(e.g.: (n^2,3n^2/(2n^2+1),3sin(n)/n^2) in R^3 or n^3 N--> R)  11. “Linear” quite literally references lines. So any function that defines a line is a linear function. In R^2, y=mx+b is a linear function, and any exponential function would define a curve so as to be nonlinear. Not sure here, but I believe that the surface of a sphere is an example of a nonlinear space. Any manifold that has a noneuclidean metric should be a nonlinear space. If a real mathematician should tell you different, then believe them.  12. Originally Posted by GiantEvil “Linear” quite literally references lines. So any function that defines a line is a linear function. In R^2, y=mx+b is a linear function, and any exponential function would define a curve so as to be nonlinear. Not sure here, but I believe that the surface of a sphere is an example of a nonlinear space. Any manifold that has a noneuclidean metric should be a nonlinear space. If a real mathematician should tell you different, then believe them.
I think linear means something that acts like line rather than being a line. remember please regression analysis.  Posting Permissions
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