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Topic: Calculus without irrational numbers
Replies: 2   Last Post: Aug 11, 2013 2:09 PM

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Posts: 160
Registered: 11/29/05
Calculus without irrational numbers
Posted: Aug 10, 2013 7:30 PM
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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.


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