I was studying at the FeMeSha 18 in Moscow around ’73. I recall being comfortable with the definition of derivative as a limit. On the other hand, the alternative definition that the instructor provided caused me no end of anxiety. Namely, he said the derivative is a number
such that
As you correctly point out, it takes a considerable amount of mathematical training to formulate precisely what the problem was. The problem was that the definition says absolutely nothing about how one could find such a “
“, or how to go about SIMULTANEOUSLY (in what sequence?) finding
Actually I am currently writing a text on constructivism, and it could be that even after all these years I would still be unable to identify the source of the anxiety were it not for the fact of having understood constructivism better recently.
Posted by: Alexandre Borovik | September 14, 2009
MK: A Childhood Story
Posted in Uncategorized
Here we go again… “Comfortable with limits,” but not understanding what they mean…
By: misha on September 27, 2009
at 5:39 am
As Bill Clinton had put it brilliantly, and when everything else about him is forgotten it will still shine, “it all depends on what ‘is’ is.” Just apply it to “for every epsilon there is delta bla-bla-bla…”
By: misha on September 27, 2009
at 11:05 pm
Human reading of mathematical formulas is directional: most people are aware of this when they use the equality sign. If one reads from left to right, the equality usually means the result of the computation, evaluation or reformulation of LHS is given by RHS. That’s why formulas like
usually look artificial.
Recently, teaching in Hebrew (with its right-to-left writing direction) I realized that the same is also true about the inclusion signs
is not the same as 
. Poor students…
By: Sergei Yakovenko on November 16, 2009
at 9:58 am