Limit of a sequence  
The limit of the sequence (a_{n}) is L if given any ε>0, there is an N>0 such that a_{n}L<ε for all n≥N. The yellow band is L±ε and the blue region correspons to those n≥N. The green dots are within ε of L and the red dots and red x's are not. The limit is L if for any given ε you must be able to move the blue region far enough to the right that there are no red x's.  


Created by David Richeson using GeoGebra. 