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**pokemon1111** D is subset of real number in p dimension

[$\displaystyle (\vec{x_{n}})$, n belongs natural number] is a subset of D

$\displaystyle \vec{x}$ belongs to D

suppose $\displaystyle (\vec{x_{n}})$, n belongs natural number converges to $\displaystyle \vec{x}$

f: D->R is cont' on D and f($\displaystyle (\vec{x_{n}})$)<= r for all n belongs to natural number

Prove that f($\displaystyle \vec{x}$)<=r

i have totally no idea about wt is happening here.

suppose $\displaystyle (\vec{x_{n}})$, n belongs natural number converges to $\displaystyle \vec{x}$

this sentence means lim n->infinity $\displaystyle (\vec{x_{n}})$ = $\displaystyle \vec{x}$?

and then that means lim n->infinity f($\displaystyle \vec{x_{n}}$) = f($\displaystyle \vec{x}$) ?

how can these help me to derive that...thank you so much