Stage 37 · Beyond (Optional)

37.5.3 The ε–δ Definition of a Function Limit

37.5 Into Real Analysis: Making Limits and Continuity Rigorous

Point 3 of 5

37.5.3 The ε–δ Definition of a Function Limit

Core idea

To keep f(x) within ε of L, it's enough to keep x close enough to a (within δ), and that's the hard-edged definition of a limit.

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 · 37.5.3 The ε–δ Definition of a Function Limit