The question is:

assume A is a proper subset of B and both belongs to R^n dimention

show that this implies sup(A)< and= sup(B).

It looks quite obvious, but I don't know how to construct the proof formally.

Thanks for help.

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- November 23rd 2009, 02:37 AMdelhaizeprove sup and inf
The question is:

assume A is a proper subset of B and both belongs to R^n dimention

show that this implies sup(A)< and= sup(B).

It looks quite obvious, but I don't know how to construct the proof formally.

Thanks for help. - November 23rd 2009, 03:43 AMHallsofIvy
Actually, you have a serious problem right from the start. While there is a standard "order" on R, there is no standard order on R^n for n> 1. And without a specific order there is no "lim" or "sup".

The statement you give is easy to prove in R but makes no sense in R^n for n> 1.