- The sequence is bounded above if there exists a real number such that .
- The sequence is bounded below if there exists a real number such that .
- The sequence is bounded if it is bounded above and bounded below.

- The sequence
is bounded below:

- The sequence
is not bounded above, i.e. for any real positive number
, there exists an
such that
. We have:

Actually, for any , we have .

Noah Dana-Picard 2007-12-28