The limit of a sequence
The limit of the sequence () is if given any , there is an 0 such that for all .
The yellow band is and the blue region correspons to those . The green dots are within of and the red dots and red x's are not. The limit is if for any given you are able to move the blue region far enough to the right that there are no red x's.
Note: To move the window, hold the shift key down while you click and drag. To zoom in or out, hold down the shift key and scroll the mouse.