Talk:Fundamental increment lemma

Plagiarism by Talman.

The identity (f(x+h)-f(x))/h = f'(x) + Q(x,h) is my (John Gabriel) identity that is proved for all smooth functions in the Historic Geometric Theorem that was realised from the New Calculus.

The slope difference function is Q(x,h) and not Q(h).

www.academia.edu/62358358/My_historic_geometric_theorem_of_January_2020

From this identity, both the derivative and definite integral can be defined:

www.academia.edu/105576431/The_Holy_Grail_of_Calculus

Also, it seems strange that he is allowed to create this Wikipedia entry given that the only supporting source is a short article by Talman. I always thought that one could not create any entry without the source being a physical book or journal?

64.99.242.121 (talk) 22:31, 30 August 2023 (UTC)

You're a funny dude John Gabriel. No, Wikipedia won't delete it because of "plagiarism". But I agree that the lemma doesn't say much and is an immediate consequence of the limit definition. 81.225.32.185 (talk) 07:14, 5 September 2023 (UTC)

I also want to add that this "lemma" is incorrect because the slope of a secant line DOES NOT depend on the existence of phi(h) or f'(a). In fact, f'(a) need not exist at all. Moreover, if a derivative exists, then the identity (f(x+h)-f(x))/h = f'(x) + Q(x,h) is provable for any smooth function f. See article above. — Preceding unsigned comment added by RealMathematician (talk • contribs) 11:46, 4 September 2023 (UTC)

Delete this article as it is incorrect.

I also want to add that this "lemma" is incorrect because the slope of a secant line DOES NOT depend on the existence of phi(h) or f'(a). In fact, f'(a) need not exist at all. Moreover, if a derivative exists, then the identity (f(x+h)-f(x))/h = f'(x) + Q(x,h) is provable for any smooth function f. See article above. RealMathematician (talk) 11:55, 4 September 2023 (UTC)