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 and ““. In retrospect, what I must have been bothered by is the non-constructive nature of this definition.
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
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