,
given any > 0, if we choose a positive integer such that , then for every , .
Hence, .
At this stage it is natural to ask the question: Can a convergent sequence have two different limits? We show in the next theorem that this is not possible.
2.2.4
Theorem:
Limit a sequence is unique.
Click here to View the Interactive animation : Applet 1.7
2.2.5
Note:
The technique used in the proof of the theorem is called the proof by contradiction.
. Since, 
, 
> 0, if we choose a positive integer 
such that 
, then for every 
, 
. 
. 
