Thursday, February 17, 2011

Microscopically intuitive FTC#1, take 2.

Last week, I added a small paragraph at the bottom of my Fundamental Theorem of Calculus proof attempt, trying to cast an intuitive view on the theorem,
based on my observation that, when focusing on one tiny interval, proving the FTC and understanding it is intuitive.
The paragraph was rushed and did not contain a much needed figure, therefore when I showed it to Tom he could not make sense out of it although I thought it was a really nice insight.
While analyzing some FTC proofs, I became even more aware of how useful this intuition was.
I also become aware that some proofs simply require one to work out each detail of their intuition rigorously and patiently and not much more.
I decided to take the time to polish my insight, and see if I can manage to explain it better.
One thing I realized is that it takes it quite an amount text to explain even the simplest ideas if ones wants to do it right...

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