http://sites.google.com/site/asdfasdf23135/ra8.JPG

By definition,

a_n->a iff

for all ε>0, there exists an integer N such that n≥N => |a_n - a|< ε

http://sites.google.com/site/asdfasdf23135/ra14.JPG

[note: also under discussion in Math Links forum]