Continuity and limits of functions of real variable
In the first lecture we introduce the notion of continuity of a function at a given point in its domain and a very close notion of a limit at a point outside of the “natural” domain.
This notion is closely related to the notion of sequential limit as introduced earlier. This paves a way to generalize immediately all arithmetic and order results from numeric sequences to functions.
The novel features involve one-sided limits, limits “at infinity” and continuity of composition of functions.
The (unfinished) notes, to be eventually replaced by a more polished text, are available here: follow the updates, this temporary link will eventually be erased.