Proving the Non-Negativity of a Decreasing Sequence with Limit 0

[Armbru35]

Analysis Proof Help!

If anyone could give me a hint on how to start this I would appreciate it! I am struggling with proofs! Thanks!

Given a sequence (asub(n))
s.t.
(i) the sequence is decreasing
(ii) the limit of the sequence is 0.
Prove rigorously that an is greater than or equal to 0 for every n contained in the natural numbers

 

[DiracRules]

$a_n\rightarrow 0$ if $\forall \epsilon >0\exists \bar{n}\backepsilon' \forall n>\bar{n}, |a_n|<\epsilon$.
Try to prove that, if $a_{\bar{n}}<0$, with a particular choice of epsilon the limit definition is not verified.
Remember to consider the fact that the sequence is decreasing