Date: Nov 11, 2012 10:06 PM
Author: Robert Hansen
Subject: Re: How teaching factors rather than multiplicand & multiplier confuses kids!

On Nov 11, 2012, at 12:39 PM, Joe Niederberger <> wrote:

> Nonsense, mathematicians tacitly understood continuity long before epsilons and deltas.

I never said understanding came all at once, nor that epsilons and deltas mark then end of the understanding of continuity.

I said that common sense is not about understanding at all.

> Zeno came up with his famous paradoxes precisely because he saw the trap laying in wait for those who tried to precisely analyze the intuitive concept that all or at least most humans are capable of imagining. The pencil illustration almost perfectly captures that intuition - no gaps.

Doesn't that simply prove what I am trying to say? Zeno had the advantage of formal reasoning. He laid a trap for those relying on common sense.

It doesn't take any imagination to watch someone not lift a pencil and agree that they didn't lift a pencil.

Bob Hansen