37.5 Into Real Analysis: Making Limits and Continuity Rigorous
Point 2 of 5
37.5.2 The ε–N Definition of a Sequence Limit
Core idea
For any error ε you name, there's some index N beyond which every term lands within that error, and that's the precise meaning of aₙ → A.
Module goal. Return to the limits you met earlier and use the ε–δ language to say exactly what "getting infinitely close" means, closing out the whole path and opening the door to higher mathematics.
eastmath.com · 37.5 Into Real Analysis: Making Limits and Continuity Rigorous · 37.5.2 The ε–N Definition of a Sequence Limit