D is subset of real number in p dimension

[ , n belongs natural number] is a subset of D

belongs to D

suppose , n belongs natural number converges to

f: D->R is cont' on D and f( )<= r for all n belongs to natural number

Prove that f( )<=r

i have totally no idea about wt is happening here.

suppose , n belongs natural number converges to

this sentence means lim n->infinity = ?

and then that means lim n->infinity f( ) = f( ) ?

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