Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.



Calculus without irrational numbers
Posted:
Aug 10, 2013 7:30 PM


Correct me if I'm wrong please.
==== It is possible to do differentiation over the rationals and (definite) integration, but the FTOC would not be true because f'=g' => f = g + C requires mean value theorem, which requires extreme value theorem to prove it, which requires the underlying field to be complete (i.e., supremums to exist in the proof of extreme value theorem).
So Calculus would exist, but FTOC would not as "antiderivative" would not be well defined.
===== Correct?



