
Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Posted:
Jun 16, 2013 7:55 PM


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 "..."
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

