
Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Posted:
Jun 17, 2013 1:28 AM


Nam Nguyen wrote: > On 16/06/2013 3:03 PM, Alan Smaill wrote: >> Nam Nguyen <namducnguyen@shaw.ca> writes: >> >>> On 15/06/2013 1:44 AM, Peter Percival wrote: >>>> Nam Nguyen wrote: >>>> >>>>> >>>>> No the inductive definition says that in your case of "{0, s(0), >>>>> s(s(0)), ... }" we'd have: >>>>> >>>>> (1) (0 e U) and (s(0) e U) and (s(s(0)) e U) >>>>> (2) (x e U) => (s(x) e U). >>>>> >>>>> In stipulation (2) it does _NOT_ say x must necessarily be finite. >>>> >>>> That is why you need a third clause that says (or has the effect that) >>>> the set being defined is the smallest such U. >>> >>> First, you should direct your technical "advice" here to Alan: that's >>> _his_ definition, _his_ defending of something, we're talking about. >> >> It's the standard definition, not mine. >> And this advice is of course correct. > > State it then in the technical language manner, as I did (1) and (2). > Let's postpone discussing anything else until you could do this. > > Remember you had "..." >
It is not a mystery. The set of natural numbers is the intersection of all those sets U such that: (1) (0 e U) (2) (x e U) => (s(x) e U).
 I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne

