37.5 Into Real Analysis: Making Limits and Continuity Rigorous
Point 4 of 5
37.5.4 The Rigorous Definition of Continuity
Core idea
When the limit at a point equals the function's value there, you can draw straight through without lifting your pen, and the function is continuous at that point.
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.
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