# Upper/lower sequence question

1. Jan 8, 2009

### transgalactic

if my sequence is

1/2,2/3,3/4,4/5 ..

why the upper sequence is 1

and lower sequence is 1 too ??

1 is not ever a member of a sequence.

i got the idea that upper sequence is a sub sequence constructed from the highest members
the closest to the upper bound

1 is not even in the sequence??

Last edited: Jan 8, 2009
2. Jan 8, 2009

### HallsofIvy

First, you don't mean "upper sequence"- there is no such thing. You may mean "least upper bound" of this sequence. Yes, every number in the sequence is less 1 so 1 is an upper bound on the sequence. Further, the sequence clearly converges to 1 (even though 1 itself is not in the sequence) so no number less than 1 can be an upper bound. 1 is the least upper bound. 1/2 is the smallest number in the sequence and so is the "greatest lower bound".

You have posted other questions about "lim sup" and "lim inf"- in case that is related to this" because this sequence converges to 1, the "set of subsequence limits" contains only the number 1. lim inf and lim sup for this sequence are both 1.

3. Jan 8, 2009

### transgalactic

there is such a thing as lower /upper sequence

http://img383.imageshack.us/img383/6550/19840671gt7.gif [Broken]