Write down what it means for as .
Also give the definition of the least upper bound
of a bounded nonempty set of real numbers.
Let () be a bounded monotonic nondecreasing sequence
and define by
=sup.
Without using the Monotone Convergence Theorem, show that
as .
Exercise.
Find the supremum and infimum
of the following sets, or say why the
supremum or infimum does not exist.