402.4A4 Continuous Function via Convergent Sequences

0:00 Introduction
0:57 Recall: Continuity via Open Neighborhoods
3:21 Turning our Neighborhood Intuition into Sequence Intuition
5:25 Statement of Sequential Continuity Theorem
8:33 Partial Proof of Sequential Continuity Theorem
13:00 Wrapup and Strategy

[Andreas.Kurniawan]

I learn convergence in math econ and wondering why the reference always refering continuity to sequence and ball (not like the definition of continuity in calculus class), then I found this video. Thanks for making it clear.

[duckymomo]

Is that why you can often can just plug in a into lim x->a f(x) just to find the limit?

I always thought it was weird that we can just define a limit by having assumed continuity without having defined it (and the reasoning being circular) and then solving for that limit when lim n->∞ f(xn) = f(lim xn)