The Fundamental Theorems of Calculus

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  • #26
mathwonk
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the prior version is what took me 40 years to appreciate and understand thoroughly, although of course i had to memorize something about absolute contuity as a grad student, which however I did not understand.

as proof of that, last year I started to tell my class the false theorem that a continuous function with derivative equal to f almost everywhere, must differ from the integral of an integrable f by a constant. fortunately we mathematicians have a 6th sense, called proof, or asking why?, that stops from such behavior, or at least causes us to corect it.
 
  • #27
JasonRox
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devious_ said:
mathwonk, I've developed the habit of selecting everything I write in a post (ctrl+A) every few minutes if I'm writing a lengthy post, and copying it (ctrl+C). That way if the browser crashes or I'm forced to relogin to post I can simply paste with minimal losses.

Maybe you should consider picking up this habit too seeing as your long posts are always excellent. :smile:
I do the same thing. Best advice for anyone.:biggrin:
 
  • #28
Galileo
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I suspected some conspiracy trying to keep us from reading mathwonk's wisdom, but mathwonk outsmarted them. :biggrin:

Thanks for the post.
 
  • #29
HallsofIvy
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It probabably happened because Mathwonk was "wrioting"!! We certainly can't have that!
 
  • #30
Galileo
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Probabably so. :tongue2:
 
  • #31
mathwonk
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briefly put, if f is only integrable, then every integral of f is also an antiderivative, but not every (continuous) antiderivative of f is an integral of f.
 

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