Re: Continuity

On 23 May 2006 05:15:56 -0700, "Robert Low" <mtx014@xxxxxxxxxxxxxx>
wrote:


Lee Rudolph wrote:
I like to tell students that "f is continuous at the point x" means
"at x, f is constant to zeroth order" just as "f is differentiable
at the point x" means "at x, f is linear to first order"; whence,
given that one has established that linear functions are continuous,
leads to the implication above.
There is little evidence they like hearing me tell them that, however.

Is there much evidence that they even hear you tell them it?

My experience is that whenever I have one of those 'Ah, I wish
somebody had explained to me like this!' moments, my subsequent
attempts to give my students the advantage I lacked invariably
culminate in great disappointment.

Student: Asks question.

Teacher: Beautiful insightful answer that might lead the thoughtful
student to understanding a counterexample...

Student: So are you saying the answer is no?

--Lynn
.

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