Working Definition of Limit

1. We state that

if we can create an as close to L like we want for all adequately large n.  Alternatively, the value of the a_n's approach L because n approaches infinity.

2. We define that

Determine if we can make an as large as we wish for all sufficiently large n.  Once again, alternatively, the value of the a_n's get larger and larger withno bound as n approaches infinity.

3.   We define that

Whether, we can make an as large and negative as we wish for all sufficiently large n.  Once again, in other words, the value of the a_n's are negative and obtain larger and larger without bound because n approaches infinity.