MAX prove question

1. Dec 2, 2008

transgalactic

An is a bounded sequence which converges to 0.
An>0 for every n.
prove that in this sequence we have a maximal member
??

again its obvious because if a sequence is descending and it converges from a positive number
to 0.
so 0 is the larger lower bound
and our first member must be the larger

how to transform it to math?

2. Dec 2, 2008

VeeEight

If it converges to 0, then finitely many members of the sequence take on a different value (that number may be small or large but it is still finite) and the rest of the terms approach 0.

3. Dec 2, 2008

transgalactic

how to prove it mathematically?

4. Dec 2, 2008

VeeEight

By combining what you and I wrote and using proper notation