transgalactic
Dec12-08, 02:40 AM
i am given a bounded sequence Xn
which follows lim(Xn+1 - Xn)=0
as n->+infinity
k=lim inf Xn
L=lim sup Xn
prove that every number from [k,L]
is a partial bound of Xn
??
k is the infimum of the group of limits of all sub sequences.
L is the supremum of the group of limits of all sub sequences.
a partial bound is a bound of a sub sequence
i cant say that every member from [k,L] is a limit of a sub sequence
because first i need to show the sub sequence
which follows lim(Xn+1 - Xn)=0
as n->+infinity
k=lim inf Xn
L=lim sup Xn
prove that every number from [k,L]
is a partial bound of Xn
??
k is the infimum of the group of limits of all sub sequences.
L is the supremum of the group of limits of all sub sequences.
a partial bound is a bound of a sub sequence
i cant say that every member from [k,L] is a limit of a sub sequence
because first i need to show the sub sequence