Hello,
My paradox proof is based on the following. As I can see, the current conception of the function differentiability is based on the statement that h in the definition of the derivative (limit) goes to zero but not equal to zero, however, the current limit in the definition of the derivative uses h=0, i.e. the limit does not depend on h at all. Therefore, based on the current conception of the function differentiability, I take the limit in the definition of the derivative as h goes to zero but not equal to zero, and compare it with the current limit in the definition of the derivative as h=0. I will post an updated proof later.
Also, I offer to try distinguishing values of slopes of functions "tangent lines" from "existing or real" rates, i.e. "nonexisting" rates that are defined by the current limit from "existing" rates which are defined by the limit as h goes to zero but not equal to zero.
Have a nice day.
Discussion of Integral calculus
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Re: Discussion of Integral calculus
Boris Lagutin
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student

 Posts: 173
 Joined: Thu Aug 28, 2014 9:17 pm
 Location: USA
Re: Discussion of Integral calculus
Hello Everybody,
I have added a summary to my foundation of the paradox (attachments, 2 pages). I think that the summary could matter for physics and engineering. I do not have free time to update the proof of the paradox.
Thank you.
I have added a summary to my foundation of the paradox (attachments, 2 pages). I think that the summary could matter for physics and engineering. I do not have free time to update the proof of the paradox.
Thank you.
 Attachments

 Updated_foundation_6.15.2017_page1.PNG (153.02 KiB) Viewed 167 times

 Updated_foundation_6.15.2017_page2.PNG (212.16 KiB) Viewed 167 times
Boris Lagutin
student
student
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