Hi Dick,

Here is a short write-up of something I remember -- edit to taste.

I worked at the MSC in Spring 1990 --- and the experience was enriching along many dimensions, especially with respect to understanding how students ended up hitting a stone wall at times because of how Math notation can confuse while intending to be intuitive -- here is one such example.

A studious Sophomore walked in saying "I cant get the right answer on this Calculus problem". So I observed him perform each step of the calculation, he did it perfectly until step n-1. Then he simplified E^{-x} to \log(x).

I asked him how he got that and he confidently said "that is the definition of Log(x)".

I told him it was not, and he confidently pulled out his class-notes saying Yes it is -- the Professor wrote it on the board.

So I asked him to show me what the Professor had written, and sure enough his notes read

"If f(x) = e^x, then F^-1(x) == log(x)"

It took me a while to explain the function inverse notation vs negative exponentiation to him --- but it illustrates how Math notation while intending to be intuitive and often confuse.

--raman

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-- Dick Furnas - 2021-05-18

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Topic revision: r1 - 2021-05-18 - DickFurnas