[FOM] A question concerning continuous functions

[Steve Stevenson]

I would like to ask the historical question. Who first talked about
continuous functions and what was their motivation? Does the
\epsilon-\delta definition arise in the early discussions? It seems to
me that there are two senses of this question: (1) Historical ---
leading up to today's understanding and (2) Current --- what do we
expect PhD candidates in analysis to know?

steve