Natural logs and infinity

While doing some calculus review it reminded me of the fact that e is defined imprecisely by its very definition. It is never possible to use the "real" e when calculating and it seems that the use of natural logs is actually a type of approximation. It may not be explicitly understood when the mathematics is applied. Many different effects cause loss of precision in computing solutions and it would seem that there is quite a bit of art in applying the solutions.

I am also wondering if it is possible to more integration of the teaching environment at MIT. They are doing very well to add value to the lectures by combining transcripts, recitations, programming examples and web formatting as well as interactive forums. It would seem that a teacher would be well served to communicate on a higher level where the utilities were integrated across the pathway. An example would be WebGL as an interface to allow the simultaneous voice, video and graphical representation of the functions as well as a web like integration of "Sage" or a similar package that recognizes equations and their decomposition to methods. I realize there are probably commercial packages that provide such effects and I have Wolfram math package from school, but I found it cumbersome and poorly integrated as it is closed. Simply a python computational interface with some recognition would be sufficient with LaTeX output to my Zim wiki. Perhaps in time a convenient web integration method will become apparent in use.

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